6294 U-003-409 .4

U. S. DEPARTMENT OF ENERGY - EXTERNAL DOSE CONVERSION FACTORS - (USED AS A REFERENCE IN O U I FS)

07/01 I88

DOE/EH-0070

100 REPORT

.

REPORTS LIB- F.M P C

A m 2 4 i991

6294 -. e . DE88-014691

. r i - CT ( 1 )

EXTE’ ‘TAL DOSE-RATE CONVERSION FACTORS FOR 4LCULATIOW OF DOSE TO THZ PUBLIC

(U.S.) Department of Snergy Washington, DC

Jul 88

c a.

?

us. National

DEPARTMENT OF COMMERCE Technical Information Service

. .

D3EIEH.0070

DOE/EH--C070

DEES.01463:

c

us. D e p t s h e n t Gt Energy Assistant Secretary for Emironment,

Office of Environmental Guidance

Washington, D.C. 20545

Safety and Xealth

and Compfiaiice

EPRODUCED ey NATIONAL TECHNIC A L INFORMATION SERVICE

US. DEPARlYENl 01 COYYERCE SPRINGFIELD. VA. 22161

000002

6294 -

- i i i Preceding page blank

COsTE:;TS

LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . v

LIST OF TASLES . . . . . . . . . . . . . . . . . . . . . . . . . . . \*

i. IKTRODECTIOY . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 1.1 Description of Esrernal Dose-Kate Con\-crsion Factors . . . 1 1.2 Adjustments to ?re\*iously Dscunientea Xethodology. . . . . . A

5 1.3 0u:line of Rcporc . . . . . . . . . . . . . . . . . . . . . I

2. CiiLCIJIhTION OF EXTERKAL DOSE- RATE FACTORS FOR PHOTOKS AKD ELECTRONS. . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Photon Dose-Rate Factors for Body Orpns. . . . . . .

2.1.1 Immersion in contaminated air. . . : . . . . . ?.1.2 Immersion in contaminated water. . . . . . . . 2.1.3 Exposure to a contaminated ground surface. . . 2.1.6 Dose-rate fac:ors for photon spectrum from

radioac:ive d?.cay. . . . . . . . . . . . . . . 2.2 Electron Dose-Race Factors for Skin . . . . . . . . .

2.2.1 Imnersion in con:amina:ed water. . . . . . . . 2.2.2 Immersion in contaminated air. . . . . . . . .

2.2.4 Dose-rate fzctors for electron spectrum fro3 2.2.3 Exposure to ri contanirratec! ground surfacz. . .

radioactive decay. . . . . . . . . . . . . . . 2.3 Effective !hse-Rs:s Factor? for Photons . . . . . . .

. . . 7

. . . 7

. . . 8

. . 12

. . . 13

. . . 16

. . 17

. . . lti

. . . 19

. . . 2 1

. . . 2 4

. . . 2 7

3. 1NPLEVIESTATIOS OF EXTER!:AL DOSE-FATE FACT9ZS FOR PHOTONS AND ELECTX0t:S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1 Radiations from Spontaneous Fission and Bremsstrahlung. 30

3.1.1 Spontaneous fission. 30 30 3.1.2 Bremsstrahlung . . . . . . . . . . . . . . . . . . .

3.2 Corrections to the External Dose-Rate Factors 31 32 3.2.1 Effects of indoor reside.-rce. . . . . . . . . . . . . 3 5 3.2.2 Effects of ground roughness. . . . . . . . . . . . .

3.2.3 Exposure during boating activities . . . . . . . . . . 36 3.2.4 Exposure to Contaminated shorelines. 37 3.2.5 Guidance on application of dose-reduction factors. . 38

3.3 External Dose-Rate Factors for Sources in Soil. 39 3.3.1 Pho:on dwse-rate factors 39

. . . . . . . . . . . . . . . . . .

. . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . . 3.3.2 Electron dosc-rzte factors . . . . . . . . . . . . . f4 0

3.G ExteLnal Dose-Ra:e Factors for Radioactive Decay Chains . . G 1

REFEXESCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

P

I I

...

iv

APPEGDIX A. TABLES OF DOSE-RATE COWEESION FACTORS FOR EXTERt:AL EXPOSURE TO PHOTC!:S AXD ELECTRONS . . . . . . . . . . . &9

51 A.l Dose-Rate Factors for Ircrnersion in Contaminated Air A.2 Dose-Rate Factors for lrrmersion in Contarnii;at.cd Vater 91 A.3 Dose-Kate Factors for Exposure to n Contaminaced Cround

Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 131

APPENDIX 8 . DIACRkYS OF RADIOACTIVE DECAY CIUtIEiS . . . . . . . . . . 171

. . . . . . .

APPENDIX C. LISTING OF THE DCSFirCTER COMPUTER CODE. . . . . . . . . 191

...

N O T I C E

THIS DOCUMENT H A S BEEN REPRODUCED FROM

THE BEST CQPY FURNISHED U S B Y THE SPONSORING

A G E N C Y ,

TAIN PORTIONS ARE ILLEGIBLE, I T IS BEING R E -

ALTHOUGH IT IS RECOGNIZED THAT CER-

LEAS8D I N THE INTEREST OF MAKING AVAILABLE

A S MUCH INFORMATION A S POSSIBLE. .

I

6294 . .

v

LIST OF FICZRES

FiRura p;l

B . l Diagrams of R a d i x c t i u e Decay Chairis. . . . . . . . . . . . . 1 7 1

LlST OF TABLES

Tsb ie

1 Organ- spec i f i c weightlng f a c t o r s f o r c a l c u l a t i o n of e f f e c t i v e dose equ iva len t s . . . . . . . . . . . . . . . . . . 28

A . l Dose-rate f a c t o r s f o r body organs .md e f f e c t i v e d o s e - r a t e i f a c t o r f o r immersion i n contaminati 1 a i r . . . . . . . . . . . 52

A . 2 Dose-rate facyors f o r body organs and e f f e c t i v e d o s e - r a t e f a c t o r f o r irnmarsion i n con tan ina ted water. . . . . . . . . . 92

A . 3 Dose-rate faac tors f o r body organs and e f f e c t i v e d o s e - r a t e f a c t o r f o r Exposure 1 m zbove contarni-cted ground s u r f a c e . . 132

6294

1 . INTK3DUCTICIl

T h i s r e p o r t p r e s c c t s a t a b u l a t i o n u f ' d o s e - race c o ~ ~ v e l - s i o n f a c t o r s for

e x t e r n a l exposure t o photons and e l e c t r o n s e m i t t e d by r a d . i o n u c l i d s s i n t h c

environment. T'nis r e p o r t was p r c 7 a r c d i n c o n j u n c t i o n r i t h c r i t e r i n f o r

l i m i t i n g dose e q u i v a l e n t s t o members o f the p u b l i c from o p e r a t i o n s of t h e

U.S. Department o f Energy ( C S Z ) . a s g i v e n i n DOE Order 5h00 .3 . " R a d i a t i o n

P r o t e c t i o n o f thr Pub1 i c and t h e Environment. " The d o s e - r a t e c o n v e r s i o n

*

f a c t o r s a r e provided f o r use by the DOE and i t s c o n t r a c t o r s i n perforining

calculG:i.ons o f e x t e r n a l dose e q i i i v a l e n t s t o a e n l c r s of the p u b l i c .

The d o s e - r a t e c o n v e r s i o n f a c t o r s f o r e x t 5 r n a l exposure t o photons and

e l e c t r o n s p r e s e n t e d i n t h i s r e p o r t a r e based on a methodo1,)gy devElopi-d a t

Oak R i d g e ( J a t i o n a l L a b o r a t o r y . ( ' I 2 ) However, a s d e s c r i b e d i n S e c t i o n 1 . 2 ,

some adjustments o f the p r e v i o u s l y documented methodology h w e been a a d e

i n o b r a i n i n g the d o s e - r a t e c o n v e r s i o n f a c t o r s i n t h i s r e p o r t .

1.1 D e s c r i p t i o n of E x t e r n a l Dose-Rate Conversion F a c t o r s

D o s e - r a t e c o a v e r s i o n f a c t o r s f o r ex:ernal espo.;urc, which a l s o a r e

r e f e r r e d t o a s d o s e - r a t e f a c t o r s , represen: the e x t e r n a l d o s e - e q u i v a l e n t

r a t e p e r u n i t c o n c e n t r a t i o n o f a radionuclide i n t h c envlroninent f o r a

p a r t i c u l a r mode o f exposure.

t h c p u b l i c i n c l u d e the f o l l o v i n g :

The exposure modes c o n s i d e r e d f o r members o f

- immersion i n a Contaminated atmospheric c l o u d ;

-. immersion i n contaminated w a t e r ; and

- exposure t o B contzminated ground s u r f a c e .

T h e s e exposure modes a l s o zre r e f e r r e d t o c z s a i r immersion, c a t e r

immersion, and ground-surface e x p c s u r e .

* T h i s r e p o r t was prepar6.d a t 9ak Ridge R a t i o n a l L a b o r a t o r y b y D . C . Kocher. v i t h thr i s s i s t a n c e o f K. F . Eckerman.

2

TIie estina:ion of rsterml dose from arbi trnry distributioris of

radiunitclidcs in Lhe environm:?nt- is J difficult. prohiem. Therefore.

simplified and idcal ized exposure coiidit ions. often are nsswneci; n;cmely.

t.lij; the distribution of sources et the location of an esposcd individuJl

is rffcctively infinite or semi-infinicc. in extent and that rhc

radionuclide conccntrntions art uniform throughout the source region. In

particular. a semi-infinite source rcgion is assumed for immrrsion in

containinat4 air, and an inf ini Le: source retior! is assumed for irnrnersion

in contarninatcd water and esposure to a contaminated ground surface.

I f we assume that an infinite or semi-infinite source region has a uniform radionuclide concentration C at time t, then the instantaneous external dose-equix-alent rate to an exposed individual at that time,

dl!(t)/dt. can be written in the general form

dH(t)/dt - C(t) x DRF ,

=here DRF dtnotes the dose-rate factor for external exposure and is independent of timc. The dose-rate factor thus is defined as the external

dose-equivalent rate per unit radionuclide concentration.

The external dose-rate factor is determined uniquely for a given

radionuclide by the radiation type (i.e., photons or electrons), the mode

of exposure (e.g., immersion in contaminated air), and th2 body organ or

combination of organs for vhich the extetnal dose-equivalent rate is

desired.

caiculation of external dose equivalents except for the radionuclide

concentration, which is estimated either by direct measurement or by use of models for environmental trdrrsport of radionuclides. The determination

of radionuclide concentrations in the environment, including their

dependence on time after a release, is beyond the scope of this report.

In comparing calculated radiaticn dbses with applicable limits for

The dose-rate factor thus embodies all aspects of the

members of the public, the quantity of interest is the annual dose equivalent, H. For external exposure, H is the integral of the instantaneous dose-equivalent rate over a time period of one year and,

from eq. (l), can be written in the general form

H - DRF x I C(t) dt .

- -6294 . -

3

1 . 2 Adjustments t.o Previously Documented Xr!f.hcdology

Some adjuc tmext:; of the previously documented methodology (”*) have

been made in caiculating the external dose-rate factors present-cd in this

seport. The adjustments to the DOSFACTER computer code used to pe:-form

the calculiitions are described a s follows.

- Cnlculncions of photon and electron dose-rate factors for the body surface have been eliminated, since the body surface does not

represent a tissue at risk from radiation exposure.

- Calculations of photon dose-rate factors for “total body,” which represent the total energy absorbed in the body divided by the body

mass, have been replaced by effective dose-rate factors for photons

a s described below. The effective dose-rate factor provides the more

appropriate quantity for use in estimating risk from both external

and internal exposures.

- Effective dose-rate factors for external exposure t3 photons have been calculated using the weighring factors for specific body organs

recommended by the International Commission on Rzdiological

Protection (‘ICRF). ( 3 ) .The effective dose-race factors presented in

this report were obtained from photon dose-rate factors for specific

organs calculated according to the methodology docwncr.ted

previously . Although dose-rate factors for skin are calculated in

this report and a weighting factor for skin has been recorrmcnded by

the ICRP for use in assessing the dEtriment to population groups (i.e., the collective dose).(4) neither the photon nor the electron

dose-rate factor for skin is included in the effective dose-rate . factors tabulated in this report. m i s approach is consistent with

the ICRP recommendation that the dose to skin be excliided in

calculating effective dose equivalents to maximally exposed individuals in critical groups of the population. ( 4 )

3

. . ” . /.

. I .

4

- The previous calculations of elc1:tron dose-rate factors for skin at i i

dcpth below the body surface of 70 pn”’ h.we been revised s1igh:ly

by assuming a depth of 7 mg/cm2. as recommended by the ICRP;(3) this

depth represents an avc’rnge value over the body iurfnce which is

appropriate for use in enuironmencal dose assessrwr.ts. Since the

density of epidermal tissuc is assumed to be 1..12 g/~rn~,(~) the

adjustment from 70 I m to 7 mg/cm2 represents a 12% decrease in the

as!;umed dcpth of radiosensitive tissues of the skin. However, in

most cases, the resulting increases in electron dose-rate factors for

skin are small (e.g., about 3% for immersion in an atmospheric cloud

of 85Kr).

rate factors for skin obtained as an average over the entire

thickness of the dermis between 50 and 1250 prn(l) have been

eliminated. since the basal cell layer of the epidermis is regarded

by the ICRF as the principal skin tissue at risk from radiation

exposure. ( 3 ) Finally, the DOSFACTER code now includes calculations

of electron dose-race factors. for skin at depchs below the body

surface of 4 , 8 . and l*O mg/c!n2. as recommnded by Vhitton;(6) these

depths represent spproprizte valucs for different parts of the body

surface. However, electron dose-rate factors for these depths of th? skin are not tabulated in this report.

In addition, the previous calculations of electron dose-

- In the previous version of the DOSFACTER code,“) electron dose-rate

factors for skin were calculated incorrectly f o r the particular case

of ground-surface exposure to radionuclides that emit high-energy

electrons. Specifically. for emitted electron energies above abo*Jt

4.5 MeV, the subroutine EGPJJD that performs numerical integrations of

eq. (25) in Section 2.2.3 of this report underestimated the electron

dose-rate factor at a depth of 70 pm by an amount that increased with increasing energy. The largest error was about 50% for enittea

electron energies near 10 MeV, which is the highest. electron energy occurring in the decay of radionuclides considered in tnis report. ( 7 )

This error has been corrected in the present calculations.

the electron dose-rate factors for skin for ground-surface exposure

are increased for only a feu radionuclides. since the electrons

emitted hy most of the radionuclides considered in this report have

However,

‘,.

6294

5

e

energie; less than 4 . 5 EicV. ( 7 )

radionuclides chat are nffectcd by the correction. the r a s u l tine

increase in the dose-rate factor j s o ~ l y a few percent or less.

because most of the electrons emitted by these radionuclides also

have energies less than 4 . 5 MeV.

Furthermore, for those few

( 7 )

- Tne output of the DOSFACTER code has been reformatted so that all.

dose-rate factors for a given exposure mode are presented i- a single

table. This table gives (1) the photon dose-rate factors for all

organs except skin. ( 2 ) the effective dose-rate factor for photons

based on the dose-rate factors for all organs except skin, and

( 3 ) the photon, electron, and photon plus electron (i.e., total)

dose-rate factors for skin:

1.3 Outline of Report

The remainder of t n i s report is organized as follows. Section 2

presents the equations used to calculate the external dose-rate factors

for photons and electrons, including photon dose-rate factors for a11 body

organs, eleccron dose-rate factors for skin, and effective dose-rate

factors for photons. This section also describes the data bases in the

DOSFACTER computer code and the other assumptions used in calculating the

dose-rate factors. Section 3 is concerned with implementation of the

methodology presented in Section 2 and includes discussions of

(1) potentially important radiations from the decay of radionuclides in

the environment that are nct taken into account in calculating the dose-

rate factors, ( 2 ) corrections that can be applied to the dose-rate factors

tabulated in this report to take into account the effects of indoor

residence, ground roughness, exposure during Soating activities, and

exposure to contaminated shorelines, ( 3 ) methods for calculating external

dose-rate factors for exposure to sources distributed with depth in soil,

and ( 4 ) application of the dose-rate factors to the important cases of

radiopuclides that decay to radioactive daughter products.

O O U C l l l _ . . .

6

Appc.iitfix A prcscnts the tables of dase-rate conversion factors for external exposure to photons and elcctrom for immersion in contnmin.iLed

air. imrncrsion in contaminated cater, and exposurc to a rontaminatrd

grocnd surface. Appendix B presents diagrams o f the parent -daughter

relationships for all decny chiins involving two cr more of the

radionuclides considered in this report. These diagrams show the hzlf-

ljves, modes of decay, and branching fractions for each decay chain.

Finally, Appendix C presents B complete listing of the version of tht.

DOSFACTER computer code used in the calculations for this report.

b

000012

7

Phot0r.s and electron: ustially are the only icportant radiatlms

emitted by radionuclides in the envi-.onmrnt that c m penetrate t iw body

surface and give a dose to radicscnsitive tissues.

the equations used to calculate the dose-rate fectors for external

exposure to photons and electrons for iminersion in contaminated air.

imncrsion in conLaminated water. and exposcre to a concaainated ground

surface. The data bases in the DOSFACTER computer code and other

assu~nptions used to obtain the results in Appendix A also are dcscribcd.

This section prc-smts

For each radiation type and exposure mode, we first present the . . dose-rate fac:or equations for specific body organs fror, monoenergetic

sourccs. These equations then are generalized to the spectrum of pnotons

or electrons arising from the most corrmon modes of radicactive decay.

i.e.. beta decay, alpha decay. and isomeric transitions. (') Fina1ly.

calculation of the effective dcse-rate factor for external expasiirs to

phrjtons is described.

In uriusual circmstanccs, spontaneous fission and bremsstrahlung also

cen produce penetrating radiations of potcntial importance to estimation

of external dose to members of the public. These processes are not taken

into account in calculating the dose-rate fsctors preseczed in this report

but are discussed briefly in Section 3.1. As discussed in Section 1, the methodology for calculating the

external dose.-rate factors for photons and electrons has been documented

previously, ( 1 ' 2 ) except for the adjustments described in Section 1.2. The

primary purpose of presenting a complete description of the methodology -in

this report is to permit an understanding of the calculetions without the

necd f w access to other documents.

2.1 Photon Dcsr-Rate Factors for Body Organs

The photon dose-race factors for body organs presented in this report

are based on Monte Carlo simulations of organ doses for a reference

individual immersed in a contaminated atnosph-eric cloud. The Monte Carlo

simulations of organ doses for immersion in Contaminated air also pro\*idr

the basis for the photon dose-rate factors for body organs for immersion

in contaminated water and esposure to a contaminated ground surface.

,

In a11 ca?culations of photon dose-rate factors. the reference

individual is assuiied to be an adult hermaphrodite of mas% 70 kg ana height 176 cm in which the shape. location, and comp2sition of most of the

kody organs cre described by Snyder et a l . The organs f o r vhich the

model of Snyder et 21. was modified for the calculations in this report

include ovaries, Uterus. breast, and red bone marrow. The dose-rate

factors i3r ovaries and uterus are based on a body mass (58 kg) and iieight

(163 cm) that &re more appropriate for an adult female, as described by

O'Brien and Sanna. '*9110)

we have assumd that the phozon dose-rate factor for breast is the average

Breast was not considered by Snyder e t a l . , and

of tne values for skin and lungs at all enereies. The descciption of red

bone marrow by Snytier et a l . assuixs thzt the skeleton is a homogeneous

mixture of bone and bone aarrov. This model has been modified, as

described by Kerr.

the trabecular bone cavizies of the skeleton. with the resul: chat bone

provides a significat amount of shielding of the red marrov for photcn

energies below about 0.2 MeV [see also Section 2.2.1 of ref. (l)].

(ll) to take into account that red marrov is located in

2.1.1 Immersion in contaminated air

, .-

,

Tor immersion in contaminated air, an exposed individual is assumed

to be standing at the boundary of a semi-infinite (i.2.. hemispherical)

atmospheric cloud with uniform source concentration. For a urit

ccncentration of socrces of monoenergetic ?hoton: ( 7 ) of emitted energy

E,, the photon dose-rate factor for boCly organ k, denoted by DRF-,, is given by

k

( 3 )

where K is a conscanc described below, pa is the density of air. and Gy is the ratio of dosc-equivalent rate i n organ k to absorbed dose rate in air for photons of energy E, and is obcairied as described b.eio*;.

k k DRFy(E,) - (~/~)(KE,/F~)G~(E,) 9

k

9

The f a c t o r KE7/pa i n e$. ( 3 ) i s t h e absorbed dose r a t e i n a i r pe r

u n i t ccncenc ra t ion of monoenergetic s o u r c e s of enerey E, i n an i r ! f in i tc . .

uniformly contaminaced atmospheric c loud of d e n s i t y p a . This f a c t o r is

obta ined from the r equ i r enen t o f conse rva t ion of energy t h a t c?;e ercrgy

emi t t ed pe r un i f vo1w.e must equa l t h e energy absorbed p e r u n i i volume

througnout t he source r eg ion and from t h e d e f i n i t i o n o f absorbed dose a s

t he energy absorbed per uni: mass of m a t e r i a l i n t he source m e l i m . ( 1 2 ) to The f a c t o r of 1 / 2 i n eq . ( 3 ) was reconxtended by Dilliaan

e s p r e s s t h e assumption t h e t t he source r eg ion is s e m i - i n f i n i t e r a t h e r than

i n f i n i t e i n e x t e n t f o r a l l emi t t ed photon e n e r g i e s . However, c a l c u l a t i o n s

by Ryman et a'l . (13) of the e f f e c t s of t h e a i r -g round i n t e r f a c e on t h e

absorbed dose ra:e i n a i r a t 1 rn above ground, which represen:; t h e

average h e i g h t of body organs f o r an i n d i v i d u a l s t and ing on th2 ground,

have shown t h a t assuming the f a c t o r o f 1 / 2 for a l l pho:on e n e r g l e s

(1) i n c r e a s i n g l y underes t imates t h e dose as t h e energy decreases below

30 keV, e . g . , by about 706 a: 10 keV and by a f a c t o r of 2 beio;. 6 keV,

( 2 ) o v e r e s t i n a t e s t he dose a t e n e r g i e s between 30 keV and 1 tiei'. but only

by about 20% nea r 70 keV and l e s s a t o t h e r e n e r g i e s . ax!

(3) underestimates. t h e dose a t e n e r g i e s above 1 MeV. b u t only by a f e w

pe rcen t . An energy-depenJer. t c o r r e c t i o n f a c t o r f o r a i r - g r o u n d i n t e r f a c e

e f f e c t s has n o t been inco rpora t ed i n the c a l c u l a t i o n s i n t h i s r e p o r t .

because t h e c o r r e c t i o n f a c t o r (1) is l e s i t han 20% a t t h e photon e n e r g i e s

of primary importance t o e x t e r n a l dose , ( 2 ) h a s been c a l c u l a t e d on ly a t

t h e s i n g l e h e i g h t above ground o f 1 m r a t h e r t han as an average ove r t he

h e i g h t of t h e exposed i n d i v i d u a l . and (3 ) docs n o t t ake i n t o account

a d d i t i o n a l p e r t u r b a t i o n s of t he r a d i a t i o n f i e l d i n a i r above ground caused

by t h e presence of the exposed i n d i v i d u a l .

The va lue o f the cons t an t K i n eq . ( 3 ) depends on c h u n i t s i n which

the d o s e - r a t e f a c t o r is expres sed . I n t h i s r e p o r t , the d o s e - r a t e f a c t o r s

f o r a i r immersion a r e g iven i n u n i t s o f mrem/y p e r pCi!m3; i . e . . t h e u n i t

concen t r a t ion of source? is assumed t o be 1 r C i / m 3 and the dose -equ iva len t

r a t e s i n body organs arc? c sp res sed i n mrem/y. Ttlcn, i f t h e d e n s i t y of air

is expressed i n g/m3 and thc energy of t h e e m i t t e d pho:on i n MCV, K is

ob:ained a s fo l lows fram the r e l a t i o n s h i p s t h a t 1 p C i o f a c t i - i c y is

3 . 7 s 10 d i s i n r e g r a t i o n s ( d i s ) p e r strco:ld: an absorbed dose of 1 r a d is

100 e r g of absorbad enere! per gram of m;l:ctriai i n t he source wditlm, acd

fJ

- . ... . . 1'

10

1 HeV of energy is 1.6 x erg:

K - (3.7 x io'' disjpCi-s)(10-2 -g-rad/erg)(1.6 x erp,/?lcV) x (10 3 mrad/rad)(3.1536 x lo7 s/y)

( A ) 7 - 1.87 x 10 g-mr.id/lS:eV-pCi-y .

Thus. the units on the right-hand side of eq.

and the dose-rate factor is obtained in units of mrein/y per pCi/m3 by

assuming a quality faccor of one for ccnverting absorbed dose in rad to

dose equivalent in rem.

based on the calculations of Eckerman et a l . (Ih) for an infinite, uniformly contaminated cloud source. Briefly, Eckermnn et al. obtained

dose-rate factors f o i different body organs from (1) organ doses from

monoenergetic sources at the body surface calculated usiAg Monte Carlo

methods by O'Bricn and Sanna '9*10) and (2) the energy spectra of scattered phr%tons in air from monoenorectic sources in an infinice, unifornly

contami1:ated atmospheric cloud cal2ulatcd by Dillman.

dose-race factors from monoenergetic sources in an atmospheric cloud were

obtained by integrating the organ doses per photon per unit area at the

body surf?ce given by O'Brien and Sann& over the spectrum of scattercd

photons in air given by Dillmen for each source energy considered.

results of these calculations in units of Sv/y per Bq/cm3 for an assumed

air density of 1.29 x 10

Table 2 of ref. (2).

Sanna ('*'') described above coniain an error which results in a systematic

underestimation of thP organ dose-rate factors for air imersion obtained

by Eckerman et a l . (14) and used in :his report. Tile dose-rate factors arc underestimated by about 10-306 depending on the organ. and the same

systematic underestimation of photon dose-rate factors occurs in the

results for water immersion and ground-surface exposure described ir l

Sections 2.1.2 and 2.1.3. The photon dose-rate factors in this report have not been corrected for this error, because revisc-d results in the

form needed far the COSF'ACTER code were not available.

National Laboratory is undertaking an effort to produce sn appropriate s ( ' t

(3) arc mrad/y per pCi/m3.

The dose-rate factors for air immersion presented in this report arc

The orczn

The

. . 3 g/m; at 0' C and 760 mm pressure &re given in

Jacob et a l . (*'I recemly noted that the calculations of O'Crien snd

(Oak Ridge

000G16 -

.

6294

11

of c o r r e c t e d photon d o s e - r a t e f a c t o r s u s i n s ?lon:e Carlo methods.) I t a l s o

is impor-tant t o bea r i n mind t h a t t h e e r r o r i n the p r e s e n t c a l c u l a r i o n s

u s u a l l y w i l l be much l e s s than any e r r o r i n neasurenents o r calcul.itiorl..;

o f r ad ionuc l ide concentr : . t ions i n t h e En\ - i roment . T h * s , :he e r r o r i n chr

d o s e - r a t e f a c t o r s gene ra l ly i s not of concern with' rcgnrd t o the accuracy

o f e s t i m a t e s of e s t e r n a l dose. '

The d o s e - r a t e f a c t o r f o r imncrsion i n contaizinated a i r i n eq . (3 ) is

expressed i n t e r m of t he r a t i o of organ dose-equiva len t r a t e t o ahsorbcd

dose r a t e i n a i r , G7, r a t h e r than d i r e c t l y i n terms of t he dose-ra:e

f a c t o r s f o r a i r immersion c a l c u l a t e d by Eckerman ec al. (14) aad documented

i n r e f . ( 2 ) , because t h i s r a t i o a l s o i s needed i n c a l c u l a t i n g organ dose-

r a t e f a c t o r s f o r immersion i n contaminated water and exposure t o a

contaminated ground s u r f a c e ( s e e Sec t ions 2 .1 .2 and 2 . 1 . 3 ) . Again. a s

da f ined i n eq .

f u n c t i o n of photon energy a r e ob ta ined from the organ d o s e - r a t e faccoi-s

f o r an i n f i n i t e c loud source c a l c u l s t e d by Eckernan e t a i . d iv ided by the

d o s e - r a t e f x t o r i n a i r , KE7/pa. f o r t he same u n i t source concen:ration. k Ths v a l u e s of Gy used i n tne p r e s e n t c a l c u l a t i o n s a r e l i s t e d i n the

f u n c t i c n subprogram FAC i n Appendix C .

organs tit 15 photon ene rg ie s between 0.01 and 10 MeV.

k

k ( 3 ) . t he va lues of GI f o r d i f f e r e n t body organs as a

' R e s u l t s a r e g iven f o r 23 body

The d e n s i t y of a i r assumed for use i n e q . (3) is 1.185 x lo3 g/m3.

Th i s va luo is appropr i a t e f o r d ry a i r a t 20' C and 750 a m p r e s s u r e , and is

about 8% l e s s than t h e d e n s i t y a t 0' C and 760 mm p r e s s u r e assumed by

Eckerman et a l .

given i n Appendix A . l a r e abou:.8% g r e a t e r t han those t h a t vould be

ob ta ined d i r e c t l y from Table 2 o f re f . ( 2 ) . The lower a i r d e n s i t y assumed

i n che presen: c a l c u l a t i o n s a l s o r e s u l t s i n s i m i l a r i n c r e a s e s i n t h e organ

d o s e - r a t e f a c t o r s f o r exposure t o a contaminated ground s u r f a c e p re sen ted

i n S e c t i o n 2 . 1 . 3 .

Thus, t h e organ d o s e - r a t e f a c t o r s f o r a i r immersion

The d o s e - r a t e f a c t o r s fo: a i r immersion i n Appendix h .1 assume

cont inuous exposure outdocrs f o r 103% of t h e t i n e du r ing a year'.

Cor rec t ion f a c t o r s which a c c w n t f o r s h i e l d i n g of photons by b u i l d i n g

s t r g c t u r c s du r ing indsor res idence a r e d i scussed i n Sec:ion 3 . 2 . 1 .

12

2.1.2 Irmersion i n contaminated water

For imTersion in conrzminatco water, an exposed individual f s assumed

to be submersed in an infinite medium with uniform source concentyation.

Thus, as with the dose-rate factor for air irrmersion in eq. (3), the

dose-rate factor for iminersion in contaminated water can be obtained from

tlre principlc of conservation of energy. However, since calculations of

organ dose-rnte factors for wzter j.mmersion, similar to those of Eckerman

et a l . 'lo) for air immersion described in Section 2.1.1, are not available

in the literacure. we further assurre that the ratio of dose-equivalent

rate for organ k to dose-equivalent rate in tissue at the body surface of - the exposed individual is the same for the two exposuie modes. Thus, for

imersion in contaminated water, the dose-rate factor for organ k is given

in terms of the ratio of organ dose-equivalent rate to absorbed dose rate

in air for air immersion, C 7 , in eq. (3) as k

where K 3 s the constant calculated In eq. (4;. pv is the density of wa:er

and i s assued. to be 0.99623 x 10

and R, are :he ratio o f energy absorptim in tissue to enerzy absorp:ion in water ( w ) and a i r (a) for emitted energy E,. respectLvely, obtained as

described below.

6 W g/m3 for a temperature of 20' C, and K, a

\ The dose-rate factors are in units of rnren/y per pCi/m3.

W a The energy-absorption ratios Ry and R, are obtained from the plirrton

mass energy-absorption coefficients. pen/p, in tissue (t). water, and air

as follows:

For both air immersion and water immersion, the emission of monoenergetic

photons uniformly throughout the source region resulrs in a continuous

energy spectrum of photons between zero energy and the emitted energy at

every point in the source region; and it is this continuous spectrum of

phatons that is incident upon the body surface. In the present

calculations, the energy-absorption ratios R, for air immersion in eq. (7)

were obtained from the calculations of Dillman. in which the ratios of

a

O O O G 1 8

6294. .

13

mass energy-absorpcioa coe.fficients in tissue? and air are zvzrzged over

the spectrum of photons in an infinite. uniformly conZmiifiaccd atmospheric

cloud. The values of R, at 25 photoii energies betvecn 0.01 aiid 10 MeV art-

listed in the subroutine CALC in Appendix C.

The mass energy-atsorption coefficient; in tissue and water are

a

nearly equal at all photon energies. Therefore, it is an excellent

approximation to evaluate the energy-absorption ratio €?, for water

immersion in cq. (6) at thc emitted energy F,. instea.' of averaging over

the spectrum of photons in an infinite, uniformlv contaminated water

medium; this approximation has been used in the present calculations.

mass energy-absorption coefficients in tissue and water at 25 photon

energies between 0.01 and lG MeV were obtained from r e f s . (16-18) and are

listed in the subroutine CALC in Appendix C.

W

The

The dose-ra:e factors for water immersion in Appendix A . 2 assume

continuous exposure for 100% of the time during a year. Phile this

assumption may De reasonable for air iriersion and ground-surface

exposure, a more reiilistic exposure time is needed for water inxersion.

An exposure tine of le is recomendcd in the absence of site-specific informat ion;

reduced by 3 faccor of 100 in estimating external dose equivalents to meLbers of the public. An aaditional carrection factor which accounts for

photon exposure uuring boating activities is discussed in Sectior, 3.2.3.

i.e.. the dose-rate fectors in Appendix A . 2 should be (19)

2.1.3 Exposure to a con tamina ted ground surface

For exposure to a contaminated ground surface, an individual is

assumed to be standing on a smooth, infinite plane with uniform source

concentration. Since cdlculations of organ dose-rete factors for ground-

surface exposure. similar tc those of Eckcrnan e t 2 1 . ('') for air

immersion described in Section 2.1.1, were not availGble at the time this methodology was developed, we have assumed that the racio of organ dose-

equivalent rate to absorbed dose rate in air at ony height abcve ground is

the sarne as the ratio C, for air immersion defined with eq. (3). Therefore, for exposure to a contaminated ground surface. the dose-rate

factor for organ k is calculated from the product o f absorbed dose rate in

k

k air ;il,ovc ground arid the ratio C;, iis

where t: is the c, .istarit c;,lcula:cd iri '9. ( I + > . - is thc- height cf the

rccepror lccation above the ground surface denoted by 0 . 9, is the paint-

isotropic spccLfic absorbed fraction(16*20) for photons in air described

belou, and r is the distance fro!n any point on the ground surface to the

receptor location.

a

a The specific absorbed fraction in air, e,, is defined as the fraction

of the emitted energy E, that is absorbed per unit mass of air at a

distance r from an isotropic point so'irce. In this report. the dose-rate

factors for exposure to a contaminaced ground surface are given in units

of mrem/y per pCi/m2.

eq. ( 4 ) . t:w specific absorbed fraction is given in units of g-l.

Therefore, from the units for the constant K in

(16) The specific absorbed fraction for photons in air is given by

where (pen/p;, and pa are the mcss energy-absorption and linear

attenuation coefficients in air, respectively. 6,, is the energy-

absorption buildup factor in air described below, and each of these

parameters is a function of the photon energy ET. specific absorbec! fraction in units of g-l, the mass energy-absorption

caefficient is given in units of cm2/g, the linear attenuation coefficient

in cm-l. and the distance r in cm.

a

In order to obtain the

The buildup factor is dimensionless. We use the Berger form of the buildup factor given by (21)

where the coefficients Ca and Da are functions of the photon energy ET. These coefficients are obtained from linear least-squares fits of eq. (10) to published buildup factors in air. (22,231

By integration of eq. (8) over an infinite ground surface using eqs. (9) and (10) and the relation

we obtain che dose-ra:e factor for orgnn k for esposure at R heiglit z

15

above a contaminatzd ground s u r f a c e in the form

the first-order exponential integqal given by

6294

m - (l/r)exp(-par> dr . (13) 4 2

The dose-rate factors in this report are calculated for :he single height

z - 100 cn (1 rn) above ground.

In implcmenting eqs. (12) and (13), mass energy-absorption and attenuation coefficients in air for 25 photon energies between 0.01 and 10 MeV were obtiined from refs. (17) and (18) and are listed in the

subroutine CALC in AFpcndix C. Values of linear attenuation coefficients

in cm-1 are obcainei? from the mass attenuation coefficients in cm2/g by

rrultiplyine by thc density of air (1.189 x

coefficient; Ca and Da in the Bereer form of the buildup factor in

eq. (10) also are listed in the subroutine CALC in Appegdis C. The

exponentizi ictegrai in eq. (13) is calculated using polynomial and

rational approximations given by eqs. 5.1.53 and 5.1.56 of ref. ( 2 4 ) .

g,’cm3). Values of the

As discussed in Section 2 . 2 . 3 of ref. (1). the use in eq. (I) of the k ratio Cy for air immersion often results in underestimates of photon

dose-rate factors for ground-surface exposure, because the radiatior. field

at’a height of 1 above ground (1) has an angular distribution that is strongly peaked in the direction almost parallel to the ground surface

(i.e., in the direction almost normal to the body surface), rather than an

isotropic angular distribution as in the case of air immersion, and

(2) has an energy distribution that is weighted more toward higher

energies for a given emitted energy than cti: energy distribution for air immersion. Recent calculations by Jacob et e l . (15) for plane sources on

the ground, which also simulate the effects of ground roughness by

locating the sources at a depth of 3 mm in soil, indicate that the photon

dose-rate factors for ground-surface exposure in this report may be

underestimated by as much as 40% for emitted photon energies above 200 keV

but may be overestimated for energies below 50 keV.

.

These results have

not been incorporated in the calculations in this report, partly for thz!

reasons discussed in Section 2.1.1 and partly because the dose-rate faccor

in eq. (12) does not incorpcrate the effects of grouncj roughness which were included in the calculazions of Jacob e t al.

The dose-rate :actors for ground-surface exposure in Appendix A. 3

assu;ne continuous exposure outdoors for 1G06 of the tine during a year.

Correction factors to the photon dose-rate factors for this exposure node

which account for shielding by building structures during indoor

residence, ground roughness, and exposure to contaminated shorelines are discussed in Sections 3.2.1, 3.2.2. and 3.2.4, respectively. Methods for

calculating external dose-rate factors for exposure to photon sources

distributed with depth in soil are discussed in Section 3.3.1.

2.1.4 Dose-rate facrors f o r photon spectmm from radioactive dTcsy

The spectrcn of photons emitted by radionuclidzs is assur~ed to

consist entirely of discrete y- and x-rays from beta deczy, alpna decay.

or isomeric- tra3sitions (e.g., see ref. ( 7 ) ] . Therefore, for a particular

radionuclide and exposure mode, the photon dose-rate factor for organ k is given in terms of the dose-rate factors for monoenergetic sources by

I ,

where f, is the intensityLof the ith photon of energy Ey i i

decay aFd;the summation includes all discrete photons in the decay

spectrum of the radionuclide. Contributions to the 'doie-rstc factors from

the continuous spectra of photons from spontaneous fission or

bremsstrahlung are not taken into account in the results tabulated in this

report but are discusseti in Section 3.1.

in number per

a i - .

17

2.2 Electron Dose-Rate Factors for Skin

This section presents the equations for the electron dose-rate

factors as a function of deptn in tissue for air immersion. water immersion, and grovnd-surface esposure. Skin is the only organ for which

electron dose-rate factors are calc;l?need in this report. Ca1cul;tions

were not performed for the lens of the eye, because the dose-rate factors

always are less thcn those for skin due to the greater depth below the

body surface of the radiosensitive tissues for the lens of the eye.

Thus, limitation of external electron dose to the skin to ensure

prevention of non-stochastic radiation effects also will prevent such

effects in the lens of the eye Electron dose-rate factors need not be

considered for any other organs, due to the relatively short range in

tissue of electrons from radioactive decay.

( 3 )

The DClSFACTER code listed in Appendix C calculates electron dose-rate

factors for four differnct depths of :he skin below the body surface: 4 ,

8, and 4 0 mg/cm2 to represent exposures of specific parts of the body. as recornended by h?hitton,(6) and 7 mg/crn2, as recornended by the ICRP. ( 3 )

Results are presented In Appendix A of this report only for the depth of

7 mg/cm2, since this depth is an average value that is appropriate for

environmencal exposures which result in relatively uniform irradiacions of

the entire body surface.

In the electron dose-rate factor equations for monoenergetic sources

in Sections 2.2.1-2.2.3, the symbol c denotes electrons in general.

in Section 2.2.&, the symbols e and specifically denote discrete

electrons from atomic de-excitation processes and continuous electrons

fron beta decay, respectively.

depth in tissue is presented first for immersion in ccntaminated water,

kacacse the Pqzation for this exposure mode contains terms that are used

in the equacion for immersion in contaminated air.

Then,

The dose-rate factor as a function of

I !

18

For immcrsion in an infinite. anifomly contaminAted water rnediua.

the electron dosc-rate facltor at depth s in tissue (t ) from n unit

concentration of sources of Konocnergecic electrons ( c ) of cnri:t.c.d cnc.rcy

E, is given by ( 2 5 )

(15)

whc.re K is the constant calcuiated in eq. ( 4 ) . pw is the density of water

and is assumed to be 0.99823 x 10

absorption in tissue to energy absorption in water for energy E,, q is a t

leakage correction factor, G, is a geometrical reduction factor defined as

the ratio of dose-equivalen: rate zt depth x in a semi-infinite tissue

mediuii :o absorbed dose rate i n the contaminated water, and rw is the mean

electron range in water for energy E,. described below.

6 W g/m3, R, is the ratio of energy

0 u t The quantities R , , G,..and q a r e

The dose-rate factor is in units of mrem/y per pCi/m3. V

The energy-absor?tion ratio R, is obtained from the electron mass

stopping powers, dE/pds. in tissue (t) and water (w) as

Since the stopping powers in tissue and water are nearly equal at all

electron energies, the ratio in eq. (16) is evaluated at the emitted

energy E,, rather than as an average over the spectrum of electrons in an

infinite, uniformly contaminated water medium. f h e mass stopping powers

in tissue and water at 25 electron energies between 0.01 and 13 I4eV were

obtained from ref. (26) and are listed in the subroutine CALC in

Appendix C. The georetrical reduction factor G, t is analogous to the ratio of

dose-equivalent rate for organ k to absorbed dose rate in air, G,, k in the

photon doqe-rate factor equations in Section 2.1. This factor is obtained

from electron specific absorbed fractions in water calculated using Monte

Carlo methods, as described by Berger. Water is assumed to be a

tissue-equivalent material, and the geometrical reductior. factor assumcs

that a semi-infinite tissue medium is in contact with a semi-infinire.

uniformly contaminated water medium. The contaminated water is trea'cd a s

semi - infinite in extent because e1ec:rons cannot penetrate through t h r

ooooz.4 __

19

6.2 9 4

body. Thus, any po in t

t he source r eg ion , and

on the body s u r f a c e is i r r a d i a t e d by only h a l f of

G, has the va lue one -ha l f a t :he body su r face .-nd t

dec reases wi th i n c r e a s i n g depth i n t i s s u e .

f a c t o r s use3 i n the p re sen t c a l c u l a t i o n s were cjbtaincd from r e f . ( 2 7 ) . and

the v a l u e s a t 25 e l e c t r o n ene rg ie s hetween 0 .01 arid 10 MeV and at 2 1

v a l u e s of t he r a t i o x / r z ( i . e . , t he depth below t h e body s u r f a c e r e l a t i v e

t o t h e e l e c t r o n range i n water ) a r e l i s t e d i n the f u n c t i o n scbprogrem G i n

AppcndLx C .

0 . 0 1 and 10 PIeV were obta ined from r e f . (26) and a r e l i s t e d i n the

sub rou t ine CALC i n Appendix C .

The g e o c e t r i c a l reduct ion

Values of t he e l e c t r o n rirnge in water a~ 25 ene rg ie s between

The leakage c o r r e c t i o n f a c t o r q accounts f o r t h e f i n i t e l a t e r a l (25) exzent of the-body s u r f a c e and is given by t h e e i e p i r i c z l formula

1 where tne parameter a depends only on the e m i t t e d energy E,. and a f o r 1 7 e l e c t r o n ene rg ie s between 0 .02 and 4 XeV and vrilues of q2 f c r

15 vil;.+s of the r a c i o x/a between 0 2nd 1 were obt2.ined from r e f . (25)

mc! a r e l i s t e d i n the f * m c t i o n subprogram C: i n Appendix C .

Valuzs of q

As noted i n Sec t ion 2 . 1 . 2 , t he d o s e - r a t e f a c t o r s f o r water i n n r r s i o n

i n Appendix A . 2 assume exposure f o r 100% o f t h e t ime , b u t a more r e a l i s t i c

exposure time ( e . g . . l%)('') should be a p p l i e d i n e s t i m a t i n g dose

e q u i v a l e n t s t o inembers of t h e pub l i c .

from exposure dur ing b o a t i n g a c t i v i t i e s are d i s c u s s e d i n Sec t ion 3.2.3.

E l e c t r o n d c s e - r a t e f a c t o r s f o r s k i n

2.2.2 Immersion in contaninzted air

For a n exposed i n d i v i d u a l s t and ing a t t h e boundary o f a serni-

i n f i n i t e , uniformly contaminated atmospheric c l o u d , w e assume t h a t t h e

e l e c t r o n range i n a i r f o r emi t t ed energy E, is less than t h e average

h e i g h t o f t h e body s u r f a c e above ground, which is t a k e n t o be 1 m.

There fo re , t he source r eg ion is assumed t o be e f f e c t i v e l y i n f i n i t e i n

ex:ent, and the e l e c t r o n d o s e - r a t e f a c t o r a t dep th x i n t i s s u e f o r

immersion i n contaminated a i r is given i n terms of t h e geometr ica l r e d u c t i o n f a c t o r G: f o r immersion i n contaminated wa te r a s (25)

. . ' . . .

20

where K is the constant calculated in eq. ( 4 ) , pa is the density of air 3 a and is assumed to be 1.18s z 10

absorption in tissue tc energy ahsorpzion in air for emitted energy E, described below, and the 1ea;:;ge correction fac:or q and the geomctricai

reduction factor G: are descrilec! in Secticr. 2.2.i.

is in units of mrem/y per p~i/m3.

g/m3, Rt/a is the ratio of energy

The dose-rate' factor

a The energy-absorption ratio Rt/a consists of two fectors. The first

factor is the ratio of mass stopplng powers in tissue and air,

which is evaluated at the emitted energy E,. The second factor, a , also

depends on the emitted energy and accounts for the variations in mass

stopping powers in tissue and air over the continiious energy spectrm of

electrons incident on the body surface for the monoenergetic soxrce of

energy E, in an infinite, uniformly contaminated atmospheric cloud. The

mass stoppifig powers in tissue and aLr at 25 electron epcrgies between

0.01 and 10 MeV and values of a at 8 electron energies between 0.01 and

2 MeV were obtained from refs. (26) and (25). respectively, and are listed

in the subroutine CALC in Appendix C.

The assumption that the source region is effectively infinite in

extent for immersion in contaminated air results in overestiaates of

electron dose-rate factors in tissue whenever the electron energy is

sufficiently high that the range is greater than 1 m iz air plus the

assumed depth of tissue below the body surface. Section 2.2.3 below. election dose-rate factors for skin at a depth of

7 mg/cm2 in tissue are overestimated for emitted electron energies above

0.36 MeV.

energy above this value and apprsaches a factor of two at the highest

As described in

The extent of overestimation increases with increasing electron

electron energies occurring in radioactive decay. ( 7 )

As noted in Section 2.1.1. the dose-rate factors for air immersion in

Appendix A.l assume exposure outdoors for 100% of the time. The effects

of indoor residence on electron dose-rate factors for skin for air

immersion are discussed in Section 3.2.1.

.*

6294

21

2.2.3 Exposure t o a cor t x j . r ? s r e d grotid surface

Tie gruxetriciil reduction factor GF used in calculating elc-ctron

dose-rate <actors as r7 function of depth in tissue for air immcrsioi: 3nd

water ir?dzersion carmat be used in ciilcuiating dos2- ri;:r fac:ors for

exposure to ii containaced ;round surface, because the geometrical

reduction factor applies only to the case of a source vo1w.e that is

efiectivcly Sezi-infiniEe in extent and is in contact with the bady

surface of an exposeci indi\?idual. Thus, the dose-rate factor for grcuri-

surfsce exposure must be obtained by explici: consideration of the

specific absorbed fraction for electrcns.

In principle, the electron dose-rate factor at any depch in tissue fcr exposure to a contaefnateb ground surface should be calculated by

considering transport of electrons in air between any source point on the

ground and the asscmed height of the body surface above ground folloved by

trans-,o:t through tissue to the assmed depth of the skj.n. However,

electron specific absorbed fractions for transport thrcuch twG different

Cedis have no: teen considered in the literatiire. sa the proklem must be

reducad to a consideration of elecr.rcn transport throl;gh a single medicin.

The calculations in :his reporc assume that exposures of the skin

occur.at a single height of 100 cm (1 m) above ground. electron transport through air .foliowed by tissue is reduced to a

consideration of transport through air alone by replacing the assumed

thickness of tissue by an equivalent thickness of air which is added to

the assumed height of the body surface above ground.

produces mere accurate results than the alternative of considering

transport through tissue alone by replacing the assumed heieh: of the body

surface above ground by an equivalent thickness of tissue, because most of

the energy loss of electrons in transport between the ground surface and the depth of skin below the body surface occurs during transport thrsrreh

1 m of air.)

depth x in tissue. the effective height z' in air above ground at which

the electron dose-rate factor in tissuc is ccllculated is given by

Consideration of

(This assutlption

Thus, for height z of the body surface above ground and

2 ' - 2 + 1.14(pt/ra)x ,

where p t and pa are the densitits of tissue and air. respectively, and the

000027 .. .

I

2 2

,-

f a c t o r l . l L jpprosimnzes the r a t i o of mass s topp in5 powers i n t i s s u e and

a i r f o r on:; e1ec:ron energy.

code a r e performed by express ing t h e d i s t a n c e s x , t. and z' i n u n i t s of

g/cm2, r a t h e r than cn . tl:c dens i ty of t i s s u e is imt used e x p l i c i t l y i n

calcu1a:ing the e f f e c t i v e he igh t z' . )

(Since t h ? c a l c u l a t i o n s i n t h e DOSFACTER (25)

The e l e c t r o n d o s c - r a t e f a c t o r i n t i s s u e ~ ? t t h e h e i g h t z' i n a i r abovr

ground def ined bv eq . (20) then is given by

a where K is the cons tan t c a l c u l a t e d i n eq . ( l a ) , R, is t h e r a t i o of mass

s topp ing powers i n t i s s u e and a i r eLpaluated a t t h e e m i t t e d energy E, [ s e e

e q . ( 1 9 ) ) . u denotes the ground s u r f a c e , 4, is t h e s p e c i f i c absorbed

f r a c t i o n f o r e l e c t r o n s i n a i r , and r is t h e d i s t a n c e frcm any p o i n t on the

ground su r face t o the r e c q t o r l o c a t i o n a t he igh t z' i n a i r above ground.

The f a c t o r of 1 / 2 accounts f o r t he i n p e n e t r a b i i i t y of t h e body t o

e l e c t r o n s . so t h a t any po in t on t h e body s u f a c e is i r r a d i n t e d by only

h a l f o f the source reg ion . The d o s e - r a t s f a c t o r is i n u n l z s of mrcm/y p e r

p c i i d .

a

An a n a l y t i c a l equat ion f o r t h e e l e c t r o n s p e c i f i c absorbed f r a c t i o n .

analogous t o eq . ( 9 ) f o r pho:ons, h-is not been d w e l o p e d . Thus, e q . (213

must be eva lua ted numerical ly usi;ig t a b u l a t i o n s o f e l e c t r o n s p e c i f i c

absorbed f r a c t i o n s . I n o rde r t o f a c i l i t a t e n m e r i c a l i n t e g r a t i o n s , we use

t h e e l e c r r o n sca l ed poin t k e r n e l , F,, developed by Berger , ( 2 5 ' 2 7 ) which is def ined i n tenus of t he s p e c i f i c absorbed f r a c t i o n by t h e equa t ion

where r Thus, s c a l i r g of t h e s p e c i f i c absorbed f r a c t i o n is accomplished by

expres s ing dis tar ices i n u n i t s of t h e e l e c t r o n range .

is t h e e l e c t r o n range f o r ensrgy E, i n t h e medium of d e n s i t y p . 0

Tables o f s ca l ed po in t k e r n e l s i n u a t e r , F,, W a r e g iven by Berger . ( 2 7 )

and t h e r e s u l t s f o r 25 e l e c t i o n ene rg ie s between 0.01 and 10 X2V and 25

va lues of t h e sca l ed d i s t ance i n wa te r , r/r:, between 0 and 1 .20 a r e

l i s t e d i n t h e subrout ine BCWD i n Appendix C . The d o s e - r a t e f a c t o r i n

eq . (21) depends on t h e e1ec:ron s c a l e d poin: k e r n e l i n a i r , F:, which is

ob ta ined from the sca l ed po in t ke rne l i n water acco rd ing t o t h e

6294

23

(25) equation

where a' is a scalin5 parameter that depends on the energy 6 , . Values of

a' f o r 6 electron energies between 0.01 and 2 KeV.vere obtzined from

ref. (25) and are listed in the subrouzine EGEUCD in Appendix C. By expressing eq. (21) in terms of the scaled pcint kernel in air

defined in eqs. (22) and ( 2 3 ) and using the element of surface area do

giver. hy eq. (11). we obtain the electron dose-rate factor ir! tissue above

ground in the form .

where

and u is the scaled distance r/ra. Again. Z ' is given by eq. (20) and

effibodles the assumed heic!it. of the bcdy surface above ground (103 cn) and the assumed de?th of the skin below the boZy surfsce (7 ng/cm2 for the

calculations presented in this report).

, 0

The integral over scaled distance u in eq. (25) is evaluated numerically using Sirepsm's rule. For values of u greater than about

1.20; the electron scaled point-kzmel and, thus, the integral in eq. (25 )

are zero.

by use of the excellent approximation that the scaled point kernel for any

energy varies linearly with u for values between 0 and 0.05. (27) u < 0.05. the previous version of the DGSFACTEP. code") incorrectly

calculated :he incegral in eq. (251, as described in Section 1.2. For a

heiihz of the body surface above ground 02 100 cm and a depth in tissue of 7 mg/cm2, scaled distances less than 0.05 correspond to emitted electron

For values of u less than 0 . 0 5 , the integration 'is facilitated

[For

; energies greater than about L . 5 MeV. (26) ] 1 .

As shown in Fig. 9 of ref. (1). calculation of electron dose-rate

factors for skin for grcund-surface exposure at a single height of 1 m

above ground provides a reasonable approximation to the dose-rate factor

averaged over the height of an exposed individual for emitted electron

i

24

energies above about 1 NeV. As rhe energy decreases below 1 NeV, however,

the dose-rate factor at 1 rn increesiiigly underestimates the value averaged

over the height o f the body. Indeed, for energies below 0.36 !'rev. the

dcsc-rate factor 2t 1 m i s zero for a depth of skin of 7 mg/cm*, based on eq. (20) and known electron ranges in air, ('') which is a particularly

inappropriate approximttion to the dose-rate factor for prtions of t?te skin closer to che ground surface.

dose to skin frcrr: exposure to e1ec:ron sources on the ground surface is

underestimated, the external dose to skin Eenerzlly will be unimportant

co:npared with the dose to othcr organs fron internal and external

exposures.

However, in cases where the externzl

As noted in Section 2.1.3, the dose-rate factors for ground-surface exposure in Appendix A.3 assume exposure outdoors for 100% of the tine.

The effec:s of indoor residence. ground roughness, and exposure to

contiininated shorelines on electron dose-rate factors for skin for

ground-surface exposure are discursed in Sections 3.2.1, 3.2.2, and 3.2.h.

respectively. Exzernal dose-rate factors for exposure to electron sources

distributed with depth in soil are discussed in Section 3.3.2.

2.2.4 Dose-rate factors for electron spectrum from raaioactive decay

The spectrum of electrons emitted by.radionuclides is assumed to

consist of (1) discrete electrons (e) from Auger and internal conversion processes following beta decay, alpha decay, or isomeric transitions and

(2) continuous electrons ( B ) from beta decay [e.g.. see ref. ( 7 ) ) .

Therefore, for a particular radionuclide and exposure mode, the electron

dose-rate factor for skin is given in terms of the dose-rate factors for

monoenergetic sources by'

where fe

number per decay, f is the intensity of the jth continuous beta 4 m transition with endDoint energy ED

is the intensity of the ith discrete electron of energy E, in i i

in number per decay. N (E) is the j 4

000030

I

I, 6294- - 25

probzbility per unit energy for emission of an electron with anergy between E and E+dE for the jth ccntinuous beta trznsjtion, obtairiel from

the Fermi :heory of bsta decay ( 2 6 ) as described below, and the summations

include all discre:e and continuous electrcns in the decay spectrum of the

radionuclide. Contributions to the dose-rate fhctors fron tho, continuous

spectrum of electrons from sponcanenus fissim are'not tdien into accont

in the results tabulated in this report but are discussed in Section 3.1. Evaluation of the second term on the right-hand side of cq. (26)

requires kcovledge of the energy distribution function for beta decay,

€Jg(E). requiricg extensive cor.iputer calculations(29' 30) which are not feasible

for the large number of radionuclides considered in this report.

we have used an approximation. developed by Evans, (31) which simplifies the calcuktion yet also yields adequate numerical accuracy (%.e., ~ C t e r

within le of the results from rigorous calculations).

The energy distrihutim funrtior. for beza decay, properly nornalized

SO that =he probability per decay that an electron is snittcd w i t h energy

betvecn zero and the endpoint is unity, is given by

A rigorous calculation of this function is a formldzble task

Rather.

(2C)

where f (E) is the statistical factor for an allowed transition, fl(E) is the correction factor for a first-forbidden unique transition, fC(Z,E) is the correction factor for the Coulomb (electrostatic) interaction, 2 is

the atomic number of the daughter nucleus, and E; is the enapoint energy. The fac:ors fo, fl, and f are dimensionless.

mass of the electron, relativistic relationships must be used for zhese

factors.

0

Because of the small rest C

The statistical factor for an allowed transition is given by

2 fo - 91.'(L. - W) ,

where V is clie total energy of the electron, 9 is the electron momentum,

and Ym is the total energy for the endpoin: of. the spectrum.

the *lec:ron kinetic energy E in MeV and the rest-mass enerejr of

0.511 !<el". the total energy and momentum are given by

In terns of

-\ ' / *

..-

26

I

W - E/0.5il + i , ( 2 9 )

The correction factor for a first-fo:-bidden unique transition (i.e.,

a transition 'octueen initial anti final nuclear states of opposite parity

and spins differing by two units of angLlrr momentum) is given by

For allnwed transitions or higher forhidden transitions, the factor f is

assuwd to be unity. 1

The simplifying approximation to the energy distribution function for 1

b,eta decay developed by Evans involves the relativistic correction factor

for the Coulomb interaction. which is written as ( 3 1 )

2 fC - 7 2 s exp(xy) Ir(i+s+iy)l , ( 3 2 )

vhrre

In eq. ( 3 2 ) . r is the complex g a m a function which. in the present . ca.lculations. is evaluated for argument z - l+s+iy using the power-series approximation

where the coefficients ck are given vLth ,.d. b . 1 . 3 4 of ref. ( 3 2 ) .

parameter y in eq. ( 3 4 ) is positive for 0 - decay and negative for B+ decay.

The

The integral over energy in the denominator of eq. ( 2 7 ) is evaluated

numerically using Simpson's rule. h s iiput to the numerical procedure,

:he integrand is calculated at 10-keV intervals between zero energy and

the endpoint energy of each beta spectrum.

c

: * . .

I .. c ' .

/

/ /

27

6294 * .s:

2 . 3 E f f e c t i v e Sose-Rate Fac tors f o r Photons

The ICRP h a s rccommenZed cha t l j m i t s on dose equivalent t c whole body

o r s p e c i f i c body organs be r e p l a c e d by ii l i m i t on the e f f e c t i v e dose

equi-.-alent from e x t c r r a l and i n t e r n a l exposures . ('1 dose equiva len t i s intended t o provide a l i m i : on risk from s t o c h a s t i c

r a d i a t i o n e f f e c t s f o r sny uniform or nonuniform i r r a d i a t i o n s of the body.

The DClE has adopted t h e ICRP r e c o m e n d a t i c n i n i ts c u r r e n t rad iRt ion

p r o t e e r i o n s t a n d a r d s f o r inembers of the p u b l i c .

A l i m i t on e f f e c t i v e .

As def ined by t h e JCR?. ( 3 * 4 ) the e f f e c t i v e d o s e - r a t e f a c t o r f o r any

of the t h r e e e x t e r n a l exposure modes considered i n t h i s r e p o r t , denoted by

DRFE, is a weighted sum of t h e d o s e - r a t e f a c t o r s f o r s e v e r a l body organs:

DRFE - C w k D R F . k ,

k

where k i s an index denot ing each organ, wk is a weicht ing f a c t o r g iv ing

the propor t ion of t h e s t o c h n s r i c r i s k r e s u l t i n g from the kLh organ under

c o n l i z i c n s of uniform whole-body i r r a d i e t i o n . end CRF' i s :he e x t e r n a l

d o s e - r a t e f a c t o r f o r . the k t h o r g m f o r the p a r t i c u l a r expcsurc mode.

1.

The o r g z n - s p e c i f i c u e i g h t i n g f a c t o r s w assigiied by tFne I G P ' ~ ) are k given i n Tsble 1. I n tlre p r e s e n t c a l c u l e t i o n s , "gonads" is essumed t o be

t h e t c s t e s , s i n c e t h e e x t e r n a l d o s e - r a t e f a c t o r s f o r t h i s organ always a r e

g r e a t e r than t h c s e f o r the o v a r i e s , and "bone s u r f a c e s " is assumed t o be

t h e s k e l e t o n .

o t h e r than those l i s t e d i n t h e table v h i t h have the h i g h e s t e x t e r n z l

d o s e - r a t e f a c t o r s , and a v e i g h t i n g f a c t o r w

ches? c r g c z s . For e x t e r n a l exposure, the organs inclucied i n t h e

"remainder" ca:egory vary v i t h photon energy.

t h i s ca tegory inc ludes b ladder . k idneys , l i v e r , marrow. and chyrr.us: bu t a t

2 HeV, b ladder 2nd l i v e r are rep laced by b r a i n and upper l a r g e intt:s '- ' L i n e .

The organ l a b e l e d "remainder" r e f e r s t o t h e f i v e organs

- 0.06 is ass igned t c l each of k

For example, a t 0.35 KcV,

It is impcirtant t o note t h a t the d o s e - r a t e f a c t c r for s k i n is not

included i n t h e e f f e c t i v e d o s e - r a t e f a c t o r c a l c u l a t e d i n t h i s r e p a r t ,

because t h e ICRP has recommended t h a t the dose t o s k i n br excluded j n

c a l c u l a t i n g e f f e c t i v e dose e q u i v a l e n t s t o maximally exposed i n d i v i b a l s i n

c r i z i c a l popula t ion groups. ('I Tnus, f o r e x t e r n a l exposure. t h e e f f e c t i v e

dose- raze faccol- r e s u l t s from photon i r r a d i a t i o n s o n l y , and t h e d o s e - r z t a

000633

28

Table 1. Organ- spec i f i c ue igh t ing f a c t o r s

f o r c a l c u l a t i o n of e f f e c t i v e

dose equ iva len t a

Organ Wk

Gonads 0.25

Breasf 0.15

Red m;.rroG; 0 .12

Lungs 0.12

Thyroid 0.03

Bone sGrfac2s 0 .03

Reniiinder 0.30

f s c r o r f o r ..kin is used p r i n c i p a l l y t o evaluate coapl iance wi th dose

1 i : n i t s f o r inai*:idual organs xhich ensure prevant ion of non-scochascic

r a d i a t i o n e f f ? c t s . However. t he ICR? a l s o has recoraenaed t h a t :he dose

t o s k i n may be included i n the e f f e c t i v e dose equ iva len r x i t h a wei;.hting

f a c t o r of 0 . 0 1 i n as.-essing the co l l ec t iv .= detr iment from esposu res o f

popu la t iov groups. The listings i n Apptndix A of e x t e r n a l dose - race

f a c t o r s f o r s k i n f o r photons p l u s e l ec t ron5 Fe rc i z i n c l u s i o n of t he dose

t o s k i n i n :he e f f e c t i v e dose equ iva ien t xizh i t s a p p r o p r i a t e weighzing

f a c c o r . i f s o d e s i r e d .

0 0 0 C 3 4

29

3 . IMPLE?lE?~T.-lTIO:J OF E<TEFCL’:AL DOSE-RATE FACTORS

FOR PHOTO!;S ASD ELECTR0;IS

The dose - r a t e conversion f a c t o r s for e s t c r n a l exposure r;) pnotails zntl

e1ec:rons t h a t r e s u l t from inplecentac ion of t he methodology presented i n

S e c t i o n 2 are l i s t e d i n ;;ppcnc!is A.

c a l c u l a t e d f o r approsima:ely 500 rad ionucl ides o f p o t e n t i a l impor:ancc i i i

environmen:cl dose ass3ssmen:s.

photons ar8d e i e c z r o n s used t o c n l c . ~ l a t e :he d o s e - r a t e fac;nrs for eJch

Dose-rate f a c t o r s hs\*e been

The energ ies and i n t e n s i z i e s o f the

radionuc1,idc *;ere obta ined fror:! a c o n p i l a t i o n o f e.:nluat.ad r n d i o ~ c - ’ . * . ~ -. . C

decay dats. ( ? ’

i n t h e DOSFXTX cod2 i t s e l f ; rhese d z t a have been d c x r i b e d i n

Sec t ions 2 . 1 - 2 . 3 and a r z given i n :he code I i s t l n y , i n ;ipFc?ndi:< C .

A l l ~ ’ h c i . d a t a requi red f o r :he c a l c u l a t i o n s a r e conczlncd

The d o s e - r a t e f a c t o r s fcr i m x r s i o n i n coi?:aninated a i r and ir:,.nersioi?

i n con:aminated r ia te r a r e gi3;en i n ur. irs of mrern/y p e r p C i . / m 3 , and the

*.*slues for exposure to a coz:;mina:ed zround su r face a r e give:] i n u r i t s o f

nrem;:; pel- p ~ i ; m z .

a i r ir?mersLon and v;h:er imzersion and ix? u n i t s o f S-/y p e r 51/. :m2 f o r

ground-sur face exposure a r e d e s i r e d , as given i n r e f s . (1) a n i ( 3 ) . then

the *.-a?:ies f o r a i r irr.mersior, and v a t e r imnersior, i n c h i s r e p o r t shouic! bc:

reduced h:; 3 f x t o r ’ of 3 . 7 :i lo3 and rhc vs;ues €or ground-sur’nce

esposure should he r e a * x c d b:: J f x t o r of 3 . 7 x 1C’.

;f ciose-rzcc f j c r o r s i n u:ii:s of s-:/: jxr 3q/c;r;? f o r

The rexir.de.- o f t h i s s e c t i o n d i s c u s s e s some poten:lsl iy importan:

c o n s i a e r n c i o n s i.n apply ing t h s d o s e - r a r e f zczo r s i n Apperciix A :o obtai:i

res1is:ic es:iratt ls o f e:.::crnal dose equi*.*alen:s Y O nembers of :he puh! ic.

These consic!erzt ions inc lude (1) penctra:ing r z d i a t i o n s from radioac:l*:a

decs:; :ha: a r c nu: :aken in:o accocn: i n tht- c a l c u l n r i o r s . ( 2 ) co:-rec:i~i?i;

chat can h e a p p l i e d co t h e d o s r - r a t e f~c:ol-s c o e a k e i n r o n c c o ~ n t t hc

efft.c:s cf i r .door r e s i d e n c e . gi-mlr:d roughncss, e:.::osurr d..:: ;.ni; boaci.i.y,

aCZi’.’lileS. cind exposilri- t o contaziniired s t in re l ines . ( 2 ) s c ~ h n d s f o r

calcu!a:icc e:.::ernnl dose-rzt’e f;.c:ors f o r c:.:imsi.irc t o so:irccs distrih..::cc!

*dyiih dc?:ii i n s o i l . And f;! ;ip:>lics:ion o f : i i i . dcts;:-rate ! ‘actors t o

i?port’:ir.:: czsc-s o f rric!icinr:c? i:!<.s :h~: c!t.co:‘ rnc!ia.7c:: d;1ui;!i:i*r

. . .

:,.-ati*xcs.

..

30

3.1 Radiations from Sponrancous Fission and Bremsstrahlung

The external dose-ra:-a factors in Appendix A take into account only

phorons and electrons from lece decay. alpha decay, and isomeric

transicions. In unusuzl circumstances. penetrating radiations from

spontaneous fission decay or bremsstrahlung ais3 could be hportant in

estimsting external dose equivalents to members of the public.

3.1.1 Spontaneous fission

Spontaneous fission occurs in the dccay of several radionuclides in

the accir,ide series, and rcsults in the emission of photons, electrons,

aid neutrons as well as fission fragments. However, spontaneous fission

is an important decay mode for only a few radionuclides (e.g., 2 4 8 C m ,

'"Cf, 25'4Cf, and 256Fm); in these cases, the dose-rate factors in this

report considerably underestimate external dose equivalents.

Brancking fractions f o r spontaneous fission for the radionuclides

considered in this report a r ~ given in Appendix 5 of rcf. (7). Empirical

relationships for the continuous energy spectra of photons, electrons, and

neutrons from spontaneous fission that could be applied to the estimation of externrl dose equivalents are given by Dillman and Jones. (33)

external dose equivalents from spontaneous fission usually will be

unimportant in dose assessments for members of the public, either because

radionuclides with significant branching fracticns for spontaneous fission

will occur in relatively small concentratims in the environment or

because dose equivalents from internal exposure will be much more

importznt for these radionuclides.

However,

3.1.2 Brcrnssrrahlung

Bremsstrahlung is the continuous spectrum of photons produced

primarily by the slowing do-dn of electrons emitted in radioactive dccn;l 1);;

interaction kith the material surrounding the radiating atom air,

vater, or soil for radionuclides in the environment). Brcinr.strnhlunC nlxo

..

\

6294 31

is produced by interaction of an eje.ct.ed electron with tlic decaying

nucleus itself, but this contribution is negligible.

usually Kill be iipor:ant in estimating external dose equivalents only for

Bremsstrahlung (30)

- radionuclides that are pure beta emitters with relatively high decay

energies (e.g.. 90Sr and its daughter 90Y). Me:hods for calculating the spectriirn of bremsstrahlung in a number of

materials have been implemented by Dillman. (30) Simplified methods, bnscd

on an approx5mation given by Evans, ( 3 1 ) have been imp1emen:ed by O'Donnell

et a l .

brensstra!ilung ssunliy will be uaimportant in dose assessments for members

of the pubiic, either because of the pr'2sence of significant

concentrations of photon-emittiag radionuclides in the environment or

because, for radionuclides that are pure be:a emitters, dose equivalents

from internal exposure will be much more important.

However, contributions to external dose equivalents from (3h!

3.2 Corrections to the External Dose-Rate Factors

This section discusses corrections that can be applied to the

external dose-rate factors for photons and.electrons in Appendix A to take

into account the effects of indoor residence, ground roughness. exposure

during boating activities, and exposure to contaminated shorelines. These

corrections, vhich are referred to as dose-reduction factors, are

multiplicative factors that are less than or equal to unity and. thus,

s e m e to reduce estimates of external dose equivalents. These factors may

be applied t o the external dose-rate factors for particular exposure modes

to obtain more realistic estimates of dose equivalents to members of the

public.

Two separate factors must be taken into account in estimating the

effects of dose-reduction factors on external dose equivalents to members

of the public: (1) rho reduction in dose during a particular exposure situation (e.g., during indoor residence) and (2) the fraction of the time during a year that the reduction in dose occurs. Thus, in estimating

annual dose equivalents. the dose-reduction factor for a particular

exposure situation must be weighted 'by the fraction of the year during

vhich the reductior! in dose is assumed to occur. Both of these factors

. . * , . .

.... ._ 03 7

\

32

are discussed in Sections 3.2.1-3.2~6.

None of the dose-reduction factors €or external exposure discussed

this section were applied to the photon and electron dose-rate factors

tabulated in Appendix A. Guidance on use of the dose-reduction factors

in

in

estimating external dose equivalents to members of the public is presented

in Section 3.2.5.

c

3.2.1 Effects of indoor residence

The dose-rate factors for immersion in contaminated air in I

Appendix A.l and exposure to a contaminated ground surface in Appendix A.3

assume that exposed individuals spend all of the time outdoors. A more

realistic dose assessment for these exposure modes would take into account

the effects of shielding by building structures in reducing external dose

equivalents during indoor residence.

Photon exposures. For routine releases from nuclear reactors, the

U . S . Nuclear Regulatory Commission (NRC) recornends that the following

dose-reduction facrors be applied in calculating external dose equivalents

from photons to take into account both the shielding provided by building

structures during indoor residence and the fraction of the time

individuhls spend indoors: (35)

Photon dose-reduction factors for air iinversion and ground-surface

exposure to account for indoor residence - - 0.7 for maximally exposed individuals; - 0.5 for average individuals i n population groups.

In both cases, the recommended shielding factor during indoor residence is

0.5. The difference in the two dose-reduction factors then reflects the

assumed fraction of the time spent indoors, i.e., about 50% for maximally

exposed individuals but nearly 100% for average individuals in population

groups. (35)

Burson and Profio. ( 3 6 )

These dose-reduction factors were based on an analysis by

Similar values, based on a compilation by

Oaklcy , (37) have been recormended ( 3 8 ) Protection and Measurements.

by the National Council on Radiation

I 0000:19

I

3 3

. .

.

The dose-reduction factors listed above may a l s o be applied to

routine releases from sources othcr than nuclear reactors and to

accidental releases. In general, howrver, the values are most appropriate

for emitted photon energies above a few hundred keV. For photons of lvar

energy, use of these dose-reduction factors may considerably overecrimatc external dose equivalents during indoor residence. (39)

The photon dose-reductLon factors for indoor residence recommended by

the NRC arebased on a shielding factor that i s representative of living

areas in single-family hoEes.

appropriate to a s s m e that exposed individuals are residing in basements

of homes o r in schools, apartment houses, or office buildings. These

structures generally provide significantly greater shielding than living

areas in single-family homes. For immersion in contaminated air, representative shielding factors range from 0.6 for the basement of a wood

frame house to 0.2 or less for a large office or industrial-type building:

and, for ground-surface exposure, representative shielding factors range

from 9.1 for the basement of a home to 0.005 for the basement of large, rndti-story StructurGs. (36)

The photon dose-reduction factors for indoor residence for ground-

surface exposure recommended by Burson and Profio ( 3 6 ) for a variety of structures and adopted by the NRC ( 3 5 ) for single-faaiiy homes take into

account activity dcposited on the outside walls and roof of the structure,

as well as activity deposited on the ground surface.

estimating dose-reduction factors for activity deposited on the outside

walls and roof of a building is given in ref. (39).

In some cases, hovever, it may be more

'

A simple model for

Electron exposures. The NRC has not considered the affects of indoor

However, since residence on external dose equivalents from electrons. (35) electrons from radioactive decay cannot penetrate building structures,

external dose equivalents from electrons during indoor residence can be

estimated on the bhsis of concentrations of radionuclides in indoor air

and on the floor of the boilding [e.g., see Section I1 of ref. ( 3 9 1 1 .

The following discussion of dose-reduction factors for electrons during indoor residence applies primarily to routine (i.e., chronic)

releases of radionuclides t o tile atmosphere, in which case steady-state

concentrztions of airborne radionuclides inside and outside buildinfis m q

be assumed. For acute or accidental relcascs. houever. the re1a:ionship I I I

'. '.

\

bctvrcn indoor and outdoor airbrirne conccntrntions of rntlionucl ides will

. .

, Y'

.-

vary vith time during and after a rrlcose. and will depend on the timing

arid extent of building ventilarion. Therefore. for such relcases. it may

be prudent LO assume no reCuction in external dose equivalents from

electrons during indoor residence. /

For noble-gas radionuclides, air immersion is the only external

exposure mode of concern. The effects of indoor residence on electron

dose equivajents to skin should be negligible during chronic releases

(i.e., the dose-reduction factor should be essentially unity), unless the

range of the emitted electrons in air is somevhat greater than the

in:erior dimensions of building rooms, because the indoor and outdoor air

concentrations for noble gases will be nearly the same.

...

For 85Kr. for example, the electron energies from beta decay are less than 0.687 MeV ( 7 )

( 2 6 ) , and the corresponding electron ranges in air are less than 2.6 m. which is a representative radius of rooms in single-family homes. dose-reztction factor of unity during indoor exposures t o electrons from

*'Kr- dtrsy is a reasonable assumption.

air is somewhat greater than the dimensions of building rooms (i .e., if

the emitted electron energy is about 1 MeV or greater), then the

assumption of a dose-reduction factor of unity will overestimate. electron

Thus, a

However. if the electron range in .

close equivalents to skin from exposure to noble gases during indoor

residence. The extent of overestimation as it depends on the electron

range in air relative to the dimensions of building rooms has not been

treated in the literature.

For depositing radionuclides, the indoor air concentration can be

considerably less than the outdoor air concentration during chronic

releases. (39 )

comparable, then the dose-reduction factcrrs for external exposure to

electrons during indoor residence can be substantial for both air

immersion and ground-surface exposure. Similar to the case of noble gases

discussed above, the dose-reduction factor for electrons for air immersion

or ground-surface exposure car! be assumed equal to the ratio oZ indoor ark

obtdoor concentrations of airborne or deposited radionuclides,

respectively, provided the electron range in air is comparable to or less

than th? dimen'sions of builtline rooms.

air, this assumption again Overestimates electrori dose equivalents to skin

Thus, if the indoor and outdoor deposition velocities are

For brcater electron ranges in

i 00004 0.

8294 3 5

during indoor residence, but by unknovn amounts.

Exposure times. As stated previously. indoor residence [ices

recommended by the NRC (35) for maximally exposed ana mirage i1:dividuals

are 50% and nearly 100%. respectively. These values apply to residence i r i

homes or apartments. Hovever. substantially lower residcncc times are

more appropriate for other locations; e.g., residGnce times of ahaiit 156

for schools and 25% for office buildings would be reasonable.

3.2.2 Effects of ground roughness

The dose-rate factors €or exposure to a contaminated ground surface in Appendix A . 3 assume that the source region is a smooth plane. A more

realistic dose assessment for this exposure mode would take in to account

the effects of ground roughness in reducing external dose equivalents,

i.e., t'e shielding provided by terrain irregularities and surface

vegetation for sources on the ground surface. A dose-reduction factor for

ground roughness vould be applied in addition to the dose-reduction factor

for indoor residence discussed in Sec:ion 3.2.1. Thus, no adCitiona1

consideration of exposure times is needed in estimating the effects of ground roug3ness on external dose eqdvalents.

Photon exposures. The NRC has not considered photon dose-reduction factors for ground-surface exposure that take into eccount g:ound

roughness. ( 3 5 )

representative of fallout folloving releases from nuclear reactor

accidents are given by Burson and Profio. (")

range from essentially 1.0 for paved areas to about 0.5 for a deeply plowed field, and a representative average value is about 0.7. case of building shielding during indoor residence discussed in

Section 3.2.1, the average dose-reduction factor for ground roughness

should overestimate extcinrl dose equivalents from ground-surface exposure

However, dose-reduction factcrs for a photon spectrum

The recommended values

As in the

if the radionuclides emit mostly low-energy photons. ( 3 9 )

Electron exposures. Eleccron dose-reduction factors for ground-

surface exposure that take into account ground roughness have not been

treated in the literature. Hovever, some reduction in dose due to terrain

irregularities and surface vegetation undoubtedly occurs. Furthermore.

. ;,.

.. . . . .

\ .

36

the electron dose is likely to be reduced by'a. greater amount due to

ground roughness than the photon dose.

dosc-rate factors for ground-surface esposure. it vould be reastnahlz to

Therefore, in -estimating elect ron

use the appropriate photon dose-reduc:ian factors for ground roughness.

since the resulting electron dose probably would not be underestimated.

fi

3.2.3 Exposure dur ing boating activities

The dose-rate factors for immersion in contaminated water in Appendix A.2 assuve ipmersion in an infinite source region and, thus, are

appropria:e f o r esposuie while swimming. conzaminated water also may occur during boating activities, but dose-

reduction factors in this case have not been considered by the XRC.

External esposure t o

( 3 5 )

Photon exposures. For photons, a dose-reduction factor of 0 . 5 during

boatint pctivlties is a reasonable value that is unlikely to underestimate

external dose equivalents. This dose-reduction factor (lj takes into account that the source region is effectively seni-infinite in extent fo r

ar. exposed individual located at the boundary of the air-vater interface

and (2) assumes tha6 the shielding of photons provided by the typically thin hull of a boat is negligible. The latter assumption vi11 result in

overestimates of external dose equivalents during boating activities for

radionuclides that emit mustly low-energy photons.

Electron esposur1:s. For electrons, it is reasonable to assume a

dose-reduction factor of zero during boating activities, i.e., that the

electron dose-equivalent rate is zero. This recommendation is based on

the assumption that the hull of a boat provides complete shielding from electron sources in the water.

Esposure times. The exposure time for boating activities should bc

estimated on a site-s?ecific basis. For individuals uho reside on a boat

for all o r part of a year, an exposure time of 50% or more would be

reasonable. For individuals who engage only in recreational boating

activities. an exposure tine as iaigh as 5% uould be reasonable.

, .. .

37

i

6294-

3 . 2 .Lc Exposure to contaminated shoreljnes

The dose-rate factors for esposure to a contJminzted grarrnd surfaces

in Appendix 4.3 assume that the source region is inzinitc in cxtcnt and,

thus, are qpropriate for large areas th;: are contaminated Ly deposition

of radionuclides from the atmosphere or by irrigation with contzcinatcd

water.

during fishing or hiking along shorelines of finite width thnt are

contaminated by deposition of radionuclides from water.

Exzernd exposure to a contaminated ground surface also may occur

( 4 0 )

Photon esposurcs.

shorelines of finite wid:h. the KRC has recoranended the following dose-

reduction factors for different types of sho:elines:

For exposure to photons from con:aminated

( 3 5 )

Phdton dose-reduction factors for exposure to contaminated

shorelines - .-

- 0.1 for discharge canal bank; - 0.2 for river shoreline; - 0.3 for lake shore;

- 0.5 for ocean shore: - 1.0 for tidal basin.

These values vould be applied in 3ddi:ion to :he dose-reduction factor far

ground roughness discussed in Section 3 . 2 . 2 , and they do not include consideration of exposure times.

Electron exposures. Dose-reduction factors €or exposure to electrocs

from contaminated shorelines have not been considered in the literature.

Because of the relatively short range of electrons in air. thc dose-rate

factor frorr. esposure to shorelines of finite width should be about the

same as the dose-rate factor for exposure to an infinite ground surface:

i.e.. t 2 dose-reduction factor for exposure to contaminated shcrelincs

should be essent'all:; unity.

electron dose-reduction factor for ground roughness. tased on an

appropriate \*slue for photons. could be t.lken into accourit i n estimating

e1cc:ron dose-rate f a c t o r s for esposure t o contaminated shorrllnes.

However. as discussed in Section 3.2.2, an

I

Exposure tin!eS. In estimating external dose cqllivolents from

shorcliric cxposure. the SRC has recormended e:;posiIre times for use in lieu

of size-specific data. ( 3 5 )

for naximallg exposed individuals and 8 hours per year for amrage

indi-:iduals in population groups. Hovever, if the dose assessmcn: takes

in:o account other age groups, then the recommcded exposure times are

considerably hiLher; i.e.. for teenagers. the recommended values are

67 hours per year fgf maximally exposed individuals and 47 hours per year

for average individuals in population groups.

The values for an adult are 12 hours pcr ycnr

( 3 5 )

2.2.5 Guidance on applicarion of dose-reduction fac tor s '

Dose-reduction factors for indoor residence, ground rocghness.

exposure during boating activities, and exposure to contaminated

shorelines have not beel used in cslculating the dose-rate factors for

ex:emal exposure to photons and electrons in Appendix A. However, dose-

redsction factors may be applied to these results at the discreciorl of

each DOE site in estimating external dose equivalents to menbers of the public. iq; use of dose-reduction factors should be fully documented:

i.e.. specific ififormation should be given regarding (1) the reduction in

external dose equivalents from photons or electrons that is assumed for a

particular exposure situation ana ( 2 ) the fraction of the time during which such dose reductions are assumed to occur.

Use of the dose-reduction factors discussed in this report is

particularly warranted whenever annual dose equivalents es:inated without

use of these fac:ors approach or exceed applicable limits. Otherwise, i t

may be unimportant that not considering the dose-reduction factors is

likely to result in overestimates of external dose equivalents for members

of :he public, because the various dose-reduction factors often will be

considerably less than the magnitude of uncertainties in measured or

calculated concentrations of radionuclides in the environment.

If dos:-reduction factors are applied to a parti.-ular exposure

sitkhtion, then it should be borne in mind that the values for photons and

electrons generally are diffcrmt. Howewr, this difference is inportant

only in estimating external dose equivalents KO the skin. because skin is

i

0 0 00 4 4

6294

39

the only organ for which the total dose may result from photon and

electron irradiations.

dose-reduction factors for skin is facilitated by the listings of photon

and electron dose-rate factors for skin in Appendix A. In estimating

external dose equivalencs to any organ except skin or in estimating

effective dose equivalents from external exposure to photons, only the

dose-reduction factors for photons vould be considered.

A separate accoun:inz of photon and electron

3.3 External Dose-Rate Factors for Sources in Soil

The photon dose-reduction factor for ground roughness discussed in

Section 3.2.2 does not describe the shielding provided by soil as radionuclides penetrate into the ground over time. e.g., by natural

infi1:ration or plowing of soils.

sources in soil nay be important in estimating dose equivalents to

max-inhlly rxposcci individuals. partlcularly\during long-term releases to

the environntenc or if the soil is ploved regularly. 0: in estimating

collective dose equivalents during the environmental residence time of th

released radionuclides. In these cases, an assunption that deposited radionuclides rznain on the ground surface usually would result in

considorable overestimates of external dose equiva1en:s.

Consideration of external exposure to

3.3.1 Photon dose-rate factors

Photon dose-rate factors in air above ground from monoenergetic

sources tkat are distributed uniformly in slab sources in soil at variou5

depths belov the ground surface have been calculated by Kocher and

Sjoretn. (")

be obtained from the k n o w photon spectra(7) according to eq. (1L).

assumption of uniformly contaminated slab sources is appropriate for

frequently plowed soils or for use vith linear comparcment models that

describe dobnkard migration of radionuclides in soil [e.g.. see

ref. ( & 2 ) ] . Only sources within about 1 m of the ground surface need to be considered, because depths of soil grea er than 1 m provife essential:

The dose-rate factors for particular radionuclides then ma:

The

40

complete shielding of photons from radioactive decay for an exposed

iiidividual standing on the ground surface.

);ocher and Sjoreen(4’) also have calcu1a:ed phcton dose-rate factors

in air above ground for monoenergetic sources that are distributed

exponentially with depth in soil.

appropriate for the case of natural infiltration of radionuclides into

soil during a chronic deposition onto the ground surface.

Such a source distribution may be

The photon dose-rate factors in air above ground for particular

radionuclides distributed in soil, calculated as’ described above, can be

converted to ,effective dose-rate factors for an exposed individual standing on the ground by using (1) the ratios of photon dose-equivalent

rates in body organs to absorbed dose rate in air as a function of emitted

photon energy listed in the function subprogram FAG in Appendix C [i.e., the quantity C, defined with eq. ( 3 ) ] . and (9) the orgar-specific weighting factors for the effective dose equivalent given in Table 1 (see

Section 2.3). However, for all radionuclides that emit significant

incensicies of photons with energies greater than a fev hundred keV. xhich

are of greatest concern in estimating external dose equi*:alents from

esposure tc contaminated s o i l , it is an excellent 2;prosima:ion to assume

chat the ratio of Affective dose-rate factor :O ths dose-rate factor in ~

air is 0.7.

k

3.3.2 Eiecrron dose-rate facrors

Esternal exposure to electrons from radionuclides dLstributed wL:h

depth in soil generally c3n be neglected. because a few cn? (and often onl:..

a few mm) of soil Frovides complete shielding of electrons from

radioactive decay for a receptor location 1 m above ground. ( 2 6 )

calculations of electron dose equix-alents from soilrces deposited on :he

ground need to consider only those sources tha: remain on or very near :I)(

T h u s ,

surface.

6294

3.k External Dose-Rate Factors for Radioactive Decay Chains

In applying the dose-rate factors for external esposure in Appendix A

to estimates of dose equivalents to nembers of the public, it is important

to understand tha: the values for each radionuclide do not include any

possible contributions from radioactive daughter products. Rather, the

tabulations contain separate entries for all such daughter produccs. For

esarrple. the photon dose-rate factors listed for 137Cs are zero. because

all photons result from the decay of the 137mBa daughter. ('I and a

separate listing of the photon dose-rate fsctors for the daughter is

provided. The parent-daughter relationships. including half-lives, modes

of decay, and decay branching fractions, €or all radionuclides considered in this report are shown in Appendix B.

In the particular case of 13'Cs decay to 137mBa noted above. it

generally is reasonable to assume that the activity of I3'%a is in

sec*:lar equilibrium with che activity of 137Cs at any locatio11 in the

enviromen: and at any time, due to the short half-life of the daughter

and the similarity in environmental behavior of the parant and daughter.

Thus, the dose-rate factors for l?'mBa can be multiplied by :he known

branching fraction"' of 0.9L6 for decay of 13'Cs to 137mEa and added to

the corresponding dose-rate factors for 137Cs.

reasonable for other decay chains involving short-lived daughter products

and parent and daugh:er radionucl ides that exhibit similar environmental

behavior (e .g., lo6Ru decay to lo6Xh).

A similar assumption is

In many pocencially impor:ant cases, however, it may nor be

reasonable to assume secular equilibrium in the environment berween a

raaionuclide and its radioactive daughter products. Esamples inqluda the

comples decay chains involving radio-bclides in the actinide series and

their radioactive daughter products. in which parent and daugh:er

radionuclides may c-shibit significant differences in environnentzl

behavior. decay chains involving noble gases and radionuclides that czn

deposit on the ground surface ( c . g . . 88Kr decay to 88Rb), and decay chain:.

in r;hich the parent and daughter radionuclides are reasonahlv long- lispd

and h a w similar half-lives (e.g., 9 5 Z r decay to 95i+b). In thesin cnscs.

the dose-rate factors for J pzrrnt and ics daughters can le combined aril:.

after p i o F r r corsideration of the equations describing production ;icd

/

0 0 0 C.4 7

6 2

decay of daughter radionuclides over time(31) and differences in

environmental behavior of the parent and daughters.

In estimating exzernal dose equivalents to members of the public,

contributions from radioactive daughters produced following a release of a

parent radionuclide to the environment generally must be considered when

the half-lives of the daughters are comparable to or less than (1) the half-life of the parent and (2) the time period of concern for the dosc. assessment (e.g.. any one-year period during the operating lifetime of a

facility). Specific examples of decay chains in which contributions from

radioactive daughters produced in the environment generally must be

considered in estimating external dose equivalents are given in the

previous two paragraphs.

such daughters that occur vith the parent in releases to the environment

also must be taken into account.

It should be emphasized that contributions from

However. in estimating external dose equivalents to members of the public during the operating lifetime of a facility (e.g.. over a period of

a fec: decades). contributions from radioactive daughters produced

folloxing a release of a parent radionuclidz to the environment generally

can be neglected if the half-life of the daughter (1) is much longer than the half-life of the parent (i.e.. by about three orders of magnitude or

more, depending on the half-life of the parent and the relative magnitudes

=f the excernal dose-rate fac:ors for the parent and daughter) (2) is

much longer than the time period of concern for the dose assessment,

regardless of the half-life of the parent.

situation would bc a release of "Mo vith a half-life of 66.02 hours

and/or "9c with a half-life of 6.02 hours, both of vhich decay to "Tc

with a half-life. of 2.13 x 10

would be a release of 23hU with a half-life of 2 . U 5 x 10 decays to 230Th vith a half-life of 7.7 x 10' years.

the activiq of the long-lived daughters produced in the environment will

be insigniticant during the time period of concern for the dose

assessment, compared with the activity of the parents released to the

environment, and the contributions to external dose equivalents from the

daughters can be ignored. (These examples are illustrative only, becausc.

the external dose fron 99Tc, 23GU, and 230Th always will be insignificant

corr;pared with the dose from internal exposures.) It again should be

An example of the first

5 years. An example of the second situation 5 years, vhich

In both examples,

0 0 0 C 4 8

e3

6294

emphasized, hovever, that long-lived daughter products also may occur wi tli

the parent in releases to the environment, in which case the daughters

mus: be considered in estinaring estrrnal dose equivalents during the

operating lifetime of a facility.

For purposes other than estimating external dose equivalents to

members of the public during the operating lifetime of a facility. the

contributions from radioactive daughter3 produced following a release of a

paren: radionuclide to the environment may need to be taken into account.

regardless of the half-lives of the daughters relative to either the

half-life of the parent or the duration of releases. For example, if the collective dose equivalent in the exposed population is to be calculated

over the residence time in the environment of the released radionuclides

and their daughters, e.g., as part of an analysis to determine if releases are A U R A (As Low As Reasonably Achievable), then in principle the

contributions from all daughters should be taken into account until

radioaczive decay is comp1e:e. The contributions from the ciaughters may

be more important than those from the parents in determining collective

dose equlva1en:s over the environmental residence time of 111

radionuclides, even when maxinun annual dose equivalents to individuals,

which occur during the release period, are determined primarily by

exposure to the parents. In praccice. however, the collective dose

equivalent may be calculated only over the operating lifetime of a

facility; or calculations beyond the operating lifetime may be truncated

by specifyins tither a time cutoff (e.g., 10,000 years) or a minimw. annual dose equivalent to individuals (e.g.. 1 mrem) for inclusion in thc collective dose.’ With such procedures, contributions to external dose

equivalenEs from long- lived daughters produced in the en-Jironmen: then

could be neglected in many cacss

The discussions in the previocs two par ?graphs illustrate the

difficulty in formulating firm guidelines reearding situacions where contributions from long-lived daughters produced in the environment either

mus: be taken into account or always can be rlcglected in calculating

ex:ernal dose equivalents to members of the public.

in calculating a x u a l dose equivalents to maximally exposed individuals

and collective dose equivalents in exposed popclations for expected

releases of radionuclides from operating facilities wiil be the most

Practical experience

. 44

usefu: means of developing appropriate guidelines.

guidelines that may be developed from practical experience also will

deFend on general procedures that are established foi performing dose

assessments. An important example discussed above is whether collective

dose equivalents are to be calculated only during the operating llfetimz

of a facility or. in addition, for an extended period of time thereafter.

However ,.- the

. oooc5o

6 2 9 4 . .

4 5

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5. International Comnission on Radiological Protection, Report o f t h e Task Grou? on Reference Man, ICRP Publication 23, Pergamon Press, .Oxford, U . K . (1975).

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h6

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2 2 .

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O O O C 5 2

- -- - -

4 7 \ 4 8

30. L. T. Dillman, EDISTR - A Computer Program t o Obtain a Nuclear Decay Data 6dSe .for Radiation Dosimetry, ORKL/TM-6689, Oak Ridge National Laboratory (1980).

3 1 . R. D. Evans, The Atomic Nucleus, Addison-Vesley. Reading, MA (1952).

32. P. J. Davis, "Gamma Function and Related Functions," p. 253 in Handbogk of Hathematical Functions, edited by H. Abramowitz and I. A . Stegun, Dover Press, New York (1965).

33. L. T. Dillman and T. D. Jones, "Internal Dosimetry of Spontaneously Fissioning Kuclides," Health Phys. 29, 111 (1975).

3L. F. R. O'Donnell, D. C. Kocher, 0. W . Burke, and F. H. Clark, CONDOS 11 - A Tool for Estimating Radiation Dosez from Radionuclide- Containing Consumer Products, NUREC/CR-2068, ORNL/NUREG/TM-456, Oak Ridge National Laboratory (1981).

35. U.S. Nuclear Regulatory Commission, Regulatory Guide 1.109. Calcularion of Annual Doses to Ean from.Routine Releases of Reactor Effluents for the Purpose of Evaluating Compliance with 10 CFR Parr 50, Appendix I (1977).

36. 2 . G. Burson and A. E. Profio, "Structure Shielding in Reactor Accidents." Health Phys. 3 3 . 287 (1977).

37. D. T. Oakley. Natural Radiation Exposure in che United States, ORP/SID 72-1, U.S. Environmental Protection Agency (1972).

38: National Council on Radiation Protection and Measurements, Natural Background Radiation in the United Scares. NCXP Report No. 45 (1975).

39. D. C. Kocher, "Effects of Indoor Residence on Radiation Dosvs from Routine Releases of Radionuclides to the Atmosphere," Nucl. Technol. 48, 171 (1980).

40. J. K. Soldat, N. M. Robinson, and D. A . Baker, Uodels and Computer Codes for Evaluacing Environmental Radiation Doses. BNWL-l7%, Pacific Northwest Laboratory (1974).

41. D. C. Kocher and A. L. Sjoreen. "Dose-Rate Conversion Factors for External Exposure to Photon Emitters in Soil," Health Phys. 48, 193 (1965) .

42. A. L. Sjoreen. 9. C. Kocher. G. ti. Killough, and C. W . Miller, ULSOIL and DFSOIL. - Computer Codes to Estimace Effective Ground Surface Concentrations for Dose Computations, OWL-5974, Oak Ridge National Laboratory (1984).

6 2 9 4 . .

Preceding page blank 49

APPENDlX A

TABLES OF DOSE-RATE CONVERSION FACTOZS FOR ESTERNAL EXPOSURE TO PHOTONS AND ELECTRONS

This appendix presents the tables of dose-rate conversion factors for

external exposure to photons and electrons.

results for immersion in contaminated air. Appendix A.2 the results f o r

immersion iE contaninated water, and Appendix A . 3 the results for exposure

to a contaminated ground surface.

Appendix A.l presents the

The tables of dose-rate factors for each of the three exposure modes

are described briefly as follows.

- Each radionuclide is identified by its name and half-life; the notation "?I" vith the radicnuclide name denotes a metastable excited

state of the isotope.

follows: S - seconds; M - sinutas; I! - hours; D - days; and Y - years.

The units for the half-lives are denoted as

- For all body organs except skin, the dose-rate factor applies to

photons only.

- The en.try labeled "EFFZCTIPE" is the effective dose-rate factor for external exposure to photons, which is a weighted sum of photon

dose-rate factors fpr 11 specific body organs, excluding skin. Tic

weighting factors applied to each organ are listed in Table 1 (see

Section 2.3).

- For skin, separate .dose-rate factors are given for photons and electrons. and the entry labeled "TOTAL" is the sum of the two. The

dose-rate factor for electrons applies to a depth in tissue below the

body surface of 7 mg/cm2.

factors for skin are nor- included in the effective dose-rate factor. Again, the photon and electron dose-rate

oooc54

50

- The dose-rate factors for all three exposure modes assume exposure for 100% of the time. Horever, as discussed in Section 2.1.2. the

values for immersion in contaminated water in Appendix A.2 should be

reduced by a substantial amount to reflect a more realistic exposure

time for members of the public. Reduction of the dose-rate factors

for this exposure mode by a factor of 100 is recommended in lieu of

site - spec if ic information.

- The dose-rate factors for each radionuclide do not include possible contributions from radioactive daughter products. The treatment of

dose-rate factors for daughter products in estimating external dose

equivale:.:s to members of the public is discussed in Section 3.6, and the parent-daughter relationships for the radionuclides cocsidered in

this report are shorn in Appendix B.

- The dose-rate factors for the three evposure modes do not take into account the effects of indoor residence, ground roughness, exposure

during boating activities, and exposure to contaminated shorelines.

Dose-reduction factors for these situations are discussed in

Section 3.2.

external exposure situations, at the discretion of the user, to

provide more realistic estimates of external dose equivaLents to

members of the public.

These dose-reduction factors may be applied to specitic

Dose-rate factors for external exposure above 'ground to radionuclides

that are distributed with depth in soil are not presenicd in this

appecdix. However, methods for their calculation are described in

Section 3.3.

The tables of external dose-rate factors listed in this appendix are

available in computer-readable form from the Engineering Physics

Information Center, Zak Ridge Niitional Laboratory, P.O. Box X , Oak Ridge,

TB 37831. Requests for these data should refer to tnc code DGSFACTER-DOE

and to this report by title and number.

. I

6294

A . l Dose-Rate Factors Cor Immersion

in Contaminated Air

The following tables give the dose-rate conversion factors for

esternal exposure KO photons arid electrons for imersion in a semi-

icfinite. uziformly contaminated atmospheric cloud. Dose-reduction

factors r;hich can Le applied to these results to trke into account

esternal esposure to a contaminated atmospheric cloud during indoor

residence are discussed in Section 3.2.1.

52

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n c) N-N m ~ i m o - 0 o - 0 * 0 a 0 0 0 0 0 0 0 0 0 0 0 0

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91

. . A . 2 Dose-Rate Factors for Imnersion

in Contaminated rater

The following tables give the dose-rate .conversion factors for

excernal exposure to photons and electrons for imersion in an infinite,

uniformly contamina:ed water medium. In lieu of site-specific data. the

dose-rate factors for this exposure mode should be reduced by a factor of 100 in estimating dose equivalents t o members of the public. Dose-

reduction factors which can be applied to these results to take into

account external exposure to contaminated water during boating activities

are discussed in Section 3 . 2 . 3 .

c z c

C' U

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Y Y . . - W W - - o m c ) 4 - 0 - e ne-- - . . . . .

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N - ~ N - . . . . .

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A . 3 Dose-Rate Factors for Exposure to a

Contaminated Ground Surface

The follouine; tables give the dose-rate conversion factors for

external expozure to phozons and electrons from an infinite, uniformly

contaminated ground surface.

1 m above ground.

Exposure is assumed to occur at a height of

Dose-reduction factors which can be applied to these

results to take into accomt external exposure to a contaminated ground

surface during indoor residence, the effects of ground roughness on

external dose equivalents, and external exposure to contaminated

shorelines are discussed in Sections 3 . 2 . 1 . 3.2.2, and 3 . 2 . & ,

respectively.

that are distributed vith depth in soil are discussed in Section 3.3.

Lose-rate factors for external exposure to radionuclides

4 : J ,

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APPEEjDIX B

DIAGRAMS OF RADIOACTIVE DECAY CHAINS

The following diagrams show the parent-daughter relationships for all

decay chains involving radionuclides considered in this report. ('I diagram gives the half-life, modes of decay, and d a a y branching fractions

for each radionuclide in a decay chain. The decay modes include a. B - , B+ and electron capture (EC). and isomeric transitions (IT). (7) distinction between EC and B+ decay is that the latter involves a total

decay energy for a transition greater than 1022 keV, so that positron

emission may occur. (7) Branching fractions are given in percent, i.e.,

number of decays per 100 ata;.~ of the parent radionuclide, and modes of

decay with branching fractions less than 0.1% arz omitted.

fraction for spontaneous fission decay, which is discussed in

Section 3.1.1. is not indicated in the diagrams.

Each

The

The branching

Ll- e- "Si (33E2 y ) - ':P( 14.29 d) - "S

0' EC "Ca - 44Sc (3.'J?7 h) - 44Ti (47.3 y)

"Sc ( 1 8.67 s)

IT 1 9/ "Ti "Sc(83.83 a)

e- 0 - "Ca (4.536 d) - "Sc (3.422 d) - "Ti

a- 0- EC 0' '*Ca (8.719 m) - '*Sc (57.4 m) "Ti - '*V (330 d)- "Cr (42.09 m)

Ll- "Fe (8.275 h) IT 1 . 7 5 1

"Mnt5.591 d )

"v (3.75 m) - "Cr

I' . c . 1 .. %

. .

0 - 0' EC ''Ha (23785 h) -"Fe - "Co (78.76 d)- '*Ni (6.10 d )

0- EC 6 "bin (I .47 m) - "Fc -"Co (270.9 d ) -'7Ni (36.08 h)

"Co (9.15 h)

"Co (1 0.47 m)

"CO ( S J i I yi

0' EC '2Ni- *'Cu (9.74 m) - "Zn (9.26 h)

,

' 9 Z ( 13 .?S h)

99.9675 y "Ca 4 (55.6 m)

EC EC - 7 J h ( 0 0 0 0 d ) - 7 ' ~ ( 7 . 1 S h)

0- 0- EC ?'GC ( I 130 h) - "& (38.2 h) - "SC - "er (57.0: h)

"Br (4.42 h)

1 7 3

8- 0 . EC "Rb(18.66d) -'% - '*Y(I4.74h)-''Zr(l65 h)

0- I' " Y ( I ~ . 6 0 d ) ~ - * ' k ( ~ . 4 d )

0- " X Z (2.24 h) - "Eb (172 P) - "9 -

I - #- I - d *'% (3.16 m) - "Zb (15.4 m).-''Sr (5055 C) - **Y (78.43 p.'

"Y (3.19 a)

. ..

174

.

, y "Nb(10.1Sd)

"Nb (3.6S7 y)

a- a- "S(2.71 h) -"Y(3.54k)-"2

"Tc ( 5 1 3 m) ,

98.0% a-

"Tc (4.28 d)

"Nb (23.35 h) -"Mo

.. . ,

, .. ..

175

- 0 - 10'Mo(14.61 m) -4-101fc(142?n) -"'Ru

"*Cd (464 d )

000180 . - - .-

176

'"Tc ( 1 19.7 C) I

000181

177

EC a- r 61% 39% - "I (12.93 d) - ' " Xc - ' "CS (1 bo m) I

EC 0- ' J a b a- ' " X t - IJaG(6.475 d) - IJaTe(78.2h)- "11(200h)-

d- 97.96'1 1.045

"Xe(2.19 d) '"Ea (38.9 t

"'I(20.8h)- 1 1 1 i/ I J'cx \ IT I 09.:

1 a J & (10.5 y: "2% ""Te (12.45 m) 'lJXe(S.245 d)

. - , I _ * 0 001 82

178

d - a- 'J4Tc(4188 m)-'J41(52.6m)-'34Xe

' "Cs (2.90 h) I

' "Cs "1 (2.062 y) Y"'"

~ " ' X I ( 1 5 J 6 m ) (28.7 h)

'"I (6.61 h)K IT 1 9 9 . 9 W y ' "C: (23E6 y) 1 83* I "Xc (9.1 1 h) ' J'Ba

"'& (18.27 m)- a- '" L (3.94 h),-."'Ce 0 - (3230 d) 1 4 1 ~

d - a- "I h ( 10.70 m) - ' " L (95.4 rn) - ' "Ce '"R(I9.13 h)-" a- 99.98 36%

d' I- EC '"G(33.0h) - "aR(13.56d) - "'Nd-"'h (265 d)

6204- - 4 7 - .

179

8 - 8 - ' "Nd ( I .73 h) 14*Rn (53.08 h)- "'Sn

8 - 8 - ' "Pm ( X i 0 h) - '"Sm (90 y) ,-.I s'Es

EC EC '"Cd- ' "Tb (150 y) - '"e (8.06 h)

000184

180

I- I' (752 h) - ' "Tm (192 y)- ' " yb I?'"

' "LV (160.10 d)

'"LJ (6.71 d)

I 'Ow-, EC I a * - 0- (90.64 h!-'''~(2.0ElS y )

II 6-95 93.25

000185

.-- _ .

"'k (33 h)

IT

6294. - .

181

"' (3r (1 3.03 h)

'"L(119d) '"R (433 a)

-1 "*Oa (30.0 h\ , g9.G,,

/ '"b EC '"R (53 y)

'"Pt (4.02 d) '"Au (30.6 I)

ITI

000186

182

000187

183

"*lh (7.34E3 y)

Ii

184

000199

185 6294 a .

186

\

000191

--u- a t 'Po (I .771 ma)

187

I . . ..

000132

188

a'* Fm (I S7.6 m)

0 1 1.1%

=*cr (2.639 y) 1 9b.9088

0 I 9 1 . y 0 1 99.9971%

"'CUI (3.JPEJ I) r'rCf (3335 d)

I - r4'R, (0.26E7 y ) a ' 'kn ( lO . l h)-'4'Cm(18.11 y)

'aan (I .iOSE IO y ) a'ru (7'

4- h) - '"Th (: I

0

(conllnu

000193

_. -_

6294

'a'fh(1.9132 y )

2aoRn(55.61 I)

II

000194

6294

Preceding page blank 191

APPENDIX C

LISTING OF TEE DOSFACTER COMPUTER CODE

This appendix gives a complete listing of the version of the DOSFACTER computer code that was used to generate the tables of external

dose-rate conversion factors f o r photons and electrons given in

Appendix A .

C C P P U X A M DOSFACTET ( D O S E FACTORS FCR EXTERNAL R A D I A T I O Y I C c A ~ D G R A M TO CALCUC'ATE DOSE-PATE c c u v E a s I o r 4 F A C T D P S F ~ P . ExTEP.vAL E x 0 n s u p . E C PHOTONS AND ELECTRONS V I A IMWEPSI?Y I N C O Y T A M f N A ~ E D A l e . I M W E J S I C W I N C CONTAMIHATEO WATER* AND i P R A D I A T ION FROM A C D Y T A M I N A T E O CP.OUND S W F A C E

C C C C C C C C C C C C C C C C C C C C

C C C C C

c c

- E L J M I N A T I O N OF PHOTON AND ELCCTPOY W S E - R A T E F A C T I P S COP THE @ODY S U I F L C E

- ELIMINATION OF PHOTON D O S E - ~ L T E FACTOPS FOR TOTAL ecoy

REPLACEMENT OF PHOTON D O S E - ? A T E FACTOSS FOR TJTAL B ~ O Y ey EFFECTIVE O I S E - R A T E FLCTORS FOR E X T E R N A L EXPCSURE; E F F E C T I V E D O S E - P A r E F S C T O P S ARE B L S E O Of4 O R G A N - S P t C I F I C W E I G H T I N G FACTDPS PECOMMENDEO I N ! C a p PURL I C A T l O N 2 5 . A N D OOSE TO S K I N IS NOT INCLUDED IN E F F E C T I V E DOSE-RATE F A C T O R S

CALCULATION OF ELECTRON DOSE-PATE F A C T O R S IN SKIN A T D E P T ~ S e r i m THE mor SURFACE OF 4. e. AND 40 M G / ( S I I CWI AND A T THE VALUE AECOMMEYDED ey THE

&NO 0.125 cn

I C R P OF 7 M G / ( S O C H I : T H E S E R E P L A C E THE P P E V I D U S C A L C U L A T I O V S F?P A D E P T H OF 0.007 C H A N D A N AVERALE OVER T H E T H I C K N E S S OF THE D E R M I S BETWEEN 0 . 0 3 5

C O R R E C T I O N OF A4 ERROR I N SUBPOLJTINE BGPNO T H A T A F F E C T S C A L C U L A T l O N OF E L E C T P C N DOSE-RATE FACTORS I N S K l N FOR GROUND SURFACE EXPOSURE FtlP. ELECTP.CN ENEPCIES WE haw1 4.5 MEV

R E F O R M A T I N G OF OUTDUT SO THLT SUYMAPY OF A L L R E S U L T S FOP E A C H €XPCl)SUf- MODE APPEARS I N A S I N G L E T A B L E - V1Z.v (11 P W T O N W S E - R A T E F d C T C R S F ' ! f

A L L D t G L N S E X C E P T S K I N S ( 2 ) E F F E C T I V E OOSE-SATE FOCTCRS F'3R P i O T O N S d'sSED ON DOSE-RATE FACTORS FOR ALL O R G I Y S EXCEPT S K I N . A1:D ( 3 1 PHOTON* ELECTPQY. A N D PHOTON P L U S ELECTRON DUSE-P.AlE FACTORS FO3 S K I N t

C PQCGRAM AUTHOR: 0. C. KCCHER C D O S I M E T P Y AND 8 I O P H Y S l C A L TRANSPORT S E C T I O N C H E A L T H AND SAFETY OESEARCH OIVISION C OAK R I D G E N A T I O N A L LAGORATOEY C C DATE: MARCH 1987 C C C I N I T I A L I Z E I N D E X FOR D E T E C T I @ N 3 F E N D - O F - F I L E FOP I N P U T D A T A C

N O U I T = D C C W R I T E H E A O I N C S FOP E A C H T A B L E OF C U T P U T C

C C PEPFDPM A C@MPLETE SET OF C A C C U L A T I 3 N S FOR 'IN€ ~ A O t 3 Y U C L I D E A T A T l * E / C C R E A D I N P U T D A T A C

C A L L P R I N T (08

000196

I

6294 193

FOR I N P U T OATA TO E N 0 C A L C U L L T I O P I S

1 C A L L O A T I N I N O U I T I C C TEST SOP. END-OF-FILE C

I F ( N O U I T .NE. CI GO TO

U R I T E I N P U T OATA

C A L L OATOUT

C A L C U L A T E O U l E - R A T E CONVERSIm F A C T O R S

C A L L CALC

WRITE OCSE-RATE C O N V E R S I O N FACTORS

C A L L OOSOUT cc TO 1

2 STOV E N 0

0001 9 7

C

C C U P I T t S M E A O l N G f FW. EACH T A B L E O F OUTPUT C C N T Y P E - I N D E X F O R E A C H T Y P E CF TABLE C = 0 FOR F I P . 5 1 T I U E THROUGH SUBROUT C Y R 1 Y T E N

SUBROUTINE P R I M I N T Y P E 1

- C C C C C C C C C C C C C C C C C C

.. - = I T O w R I T E H E A O I N G S FOP P A O I O N U C L I O E A N 0 SPECTRAL 1 O E Y T I F ~ C A T l O U

I N P U T D A T A T A B L E ONLY 2 TO W R I T E H E A O I N G S FOR B E T A - P I R T I C L E I N P U T D A T A T A B L E 3 H Y

= 3 TO WRITE H E A O I N C S FOR P O S I T R O N I N P U T OATA T A 8 L E ONLY = 4 T O W R I T E H E l O I N G S FOR AUGER AND I N T E R N A L C O N V E R S I O N ELECTOON I N P U T

= 5 TO W R I T E H E A O I N C S FOR PHOTON l N P U T DATA T A B L E ONLY D A T A T A B L E ONLV

6 T O W R I T E H E Q O I N G S FOR SUM'4AAY T A B L E S OF PHOTON DOSE-RATE FACTQRS FOR A L L G I G I N S EXCEPT S K I N . PHOTON P L U S ELECTPON DOSE-RATE FACTORS FOR S K I N . A N 0 E F F E C T I V E W S E - R A T E FACTORS FOR EACH EXPOSURE MODE

D I F F E R E N T D E P T H S I N S K I N FOA EACH EXPOSUAS MOOE 0 7 T O W R I T E H E A O I N G S FOP T A B L E S OF ELECTRON DOSE-RATE FA:TORS SO9

= 8 T O WRITE H E A O I N C S FOP TABLES OF DOSE-RATE FACTW.S FOP S K I N FO? PHOTDWSI ELECTRONSs AN0 P a T O N S P L U S ELECTRONS F O a E A C H E X P j S J R E UOOE

T H R E E EXPOSURE MODES - 9 T O W R I T E H E A O I N G S . F O R T A B L E O F E F F E C T I V E DOSE-RATE F A C T O R S FOS A L L

C I F [ N T Y P E .EO. 01 GO T O 1 GO TO ( 1 9 2 , 3. 4. 5 1 6 . 7. Be 91. NTYPE

C C R A O I O N U C L I O E A N 0 S P E C T R A L I O E N T I F I C A T I O N C

1 WRITE t 1 0 r t O l

' W R I T E I I O ~ i O l

W R I T E (10.211

W R I T E l10.tZI

W R I T E (10.231

I O F O R K A T ( I H l I

20 FORMAT I I H O . 2 x 1 4 O H R A O I O N U C L I C E AND SPECTRAL I O E Y T I F 1 C A T I O Y ~

21 FOP.r4T (1HOi 4 Z X r 24HNUUBER OF SPECTRAL L I N E S 1

2 2 SORMA? . 3 4 ~ . 39+------ _-__ ----___---------------- I

2 3 F O R H A T ( I N , 5X. T H N U C L I D E I 0X. 9 H H A L G L I F E r 5 X r SH3ETAS. 4X. 2 9HPOSITRONSo 2X. 9 H E L E C T R a Y S . 3X. 7HPHOTONS/ l

I F ( N T Y P E .NE. 01 GO T O 99 C

C c BETA-PCRTXCLE D A T A

2 W P I T E ( 1 1 ~ 1 O l WRITE ( 1 1 , 2 4 1

2 4 FORHAT I I H D . 2 x 1 4 T b l E N E P C I E S APlD I N T E N S I T I E S FOR E L C H BETA P A r r I C L 2E I

WPITE (11.251

WRITE (11.261 25 FORMAT 1 I H O i 3CX. THUAXIMUHI 9x1 T H ~ V E E A G E I 9x1 9 W I N T E N S I T Y 1

Ze F@RWAT (In s 5x9 TFMUCL;DEr ex. 9 H H A L F - L I F E , 51. I Z H E N E P G Y I Y f V I ,

195

2 4 1 . IZHENERGY t H E V 1 . 5 X . I I w t P E P O E C A y l l IF ( N T Y P E .NE. 01 GO T O 99

C c POSIfRON D A T A C

3 U P I T E t l Z . ! O I WR I TE t 1 2 2 1 I

U R I T E (12.25) YRITE 1li.?bl I F ( N T I P E .NE. 01 GO TO 99

21 FOPMAT (1HO. 2 X . 4ZHE!4EPCIES AND 1 N l E N S I T l E S . F O R E A C H P O S l l R O Y l

C C AUGER A N 0 I N T E R N A L CONVERSION ELECTP.ON DATA C

4 Y R l T E 113.101 , W R I T E 113.281 28 FORMAT t IHO. Z X r , 7 2 H E N E R G I E S AN0 I N T E N S I T I E S FOR EACH W C E R AVO I N

ZTERNAL C O W E R S 107 E L E C T R O N 1 W R I T E i 1 3 . 2 9 1

U R I l E t i 3 . 3 0 1 29 FORMAT 1IHO. 3 7 X . 6HENERCYe 9 X . 9 H I H T E N S I T Y l

3 C FORRAT t I H SX. 7 H J U C L I D E . 8 X r 9 H H A L F - L I F E e 9 X a 5 H I M E V l . B X . 2 I l H l P E R DECAY11 IF I N T Y P E .NE. 01 GO TO 99

C C PHCTON O a T A C

5 WRI 7E t 16. 101 W R I T E ( 1 4 r 3 1 l

WRITE (lSrZ91 W R I T E ( 1 4 r 3 0 I

3 1 FORMAT ( L H O , 2%. 4 0 H E N E R G S E S AN0 I N T E N S S T I E S FOU E A C H P H O T W I

I F lNTYPE .NE. 08 GO TO 99 C C DOSE-RhTE FACTORS FOR A L L OPCANS P L U S EFFECTIVE OOC,E-RATE FACTSo. C C A I R !F!MERSIO:d C

6 W R I T E 115.101 WRITE I l S r 4 1 I

41 F O f H A T t 1 H O v 2X . 9EHOOSE-RATE FACTORS FOP BODY ORGANS A N 0 E F F E C T I V ZE DOSE-RATE FACTOR FOR IMMERSIO?4 I N CWTAP4INATEO A I R 1

WRITE ( 1 5 . 4 2 )

WRITE 1 1 5 . 4 3 1

W R I T E (15.641

W R I T E ( 1 5 . 4 5 1

LZ FORMAT IIH . SX. M H I N MREWYR PER IIC~OSU~IE~~CUBI~ H I )

43 FORMAT (1H01 9 t X . SHUPPER. 6 X . SHLO3ERI

44 FORMLT I l H B l X . 3HSMALLo 6 X e 5WARGE. 6x1 W L A R G E I

4 5 FORMAT 11H 9 1x0 7WWLIOE. 4X. %HALFLIFE. 3X. BCUOREMACSr 4x9 2 ?HBLADDER. SXa SHSZlAIN. 5X. 6HBREAST. 6X. 5 H M E A R f r 4X. 3 P~INTESTINE* Z X . 9 M I N T E S T I N E m 2X. 9 H l N T E S T l N E r 3 x 1 7 H K I O N E I S l I

Y f I T 5 (16.10) WRITE ( 1 6 . 4 1 ) W R I T E 116.421 WC I T E t lo. 4 6 1

W R I T E ( 1 6 0 4 ? l 46 FORMAT ( I H O . 6fK. 3HREDl

* ? FOaMAT L l H 0 1x1 7 M U C L I O E r 4 x 1 PWHALF-L IFE . 5x9 S M I V E D . 6 x 1

000199

196

z snLuric;. sx, ~MAOROU. s x r o r ' m p a o w . sx . r n 9 v m i E s . 3xr 3 BHPANCKEASr 3X. BHSKELETONr 4 A . 6HSPIFE?I . 5 X r ?HSTOHACH/)

W R I T E 117.101 W R I T E l 1 1 r 4 1 ) W R I T E l 1 7 r 4 Z l W P I T E 117.601

W R I T E 117.611 b o FOPMAT l l H O r 8 1 x 1 411SKItJ. lX. 4 H S K I N r T X r 4 H S K l N I

61 FORMAT I I H 1X. 7)(NUCLIOE, 4 x 1 9 H H d L F - L I F E e 4 X e 6 H T E S f E S . SX. Z 6 H T H V W S r S X . THTHYPOIGr 4 X e 6HUTERUS. * I t S H E F F E C T I V E r Z X r 3 B H ( P H O T O N 1 r ZX. l O H ( E C E C T R O N 1 e 3 X r l H l f O T A L I / 1

C c WATER I M M E R S I O N C

Y R I TE (20.101 W R I T E 120.481

48 F C W A T ( I M O . ZX . LOOF(OOSE-RI'E F A C T O R S FOP 8OOY O R G A N S ARD E F F E C T ! 2 V E DOSE-RATE FACTOR FO't I W E f R S I O N I N C O N T A M I N A T E D WATER1

W R I T E 1 2 0 r 2 2 l W I T € (20.431 W P I T E I Z O r C C ) waiiE i i o 1 4 s i W I T € 121.1ot W R I T E i z i r ' r a i W P I T E l2lr4ZI WP.1TE l Z l r 4 6 ) WRITE l21.57J WP.ITE I t Z . 1 0 ~ W P I T E f 2 2 r 4 8 1 WRITE 1221421 W R I T E I22r6O) W R I T E lZir61J

c . C GROUND SURSACE EXPOSCRE

'C WP.iTE ( 2 5 1 101 WPlfE 125149)

40 FORMAT I I H O . Z X r lISHDOSE-R&TE FACTORS FOR BODY 0 9 G A N S AND E F F E C T ! 2 V E DOSE-RATE FACTOR F O B . E X F 0 S U R E I M ABOVE C0:JTAMINATED CROUNO SUR 3 F A C E )

W R I T E ( 2 5 r S O I S O FORMkT I l H r 5x1 3bHIN MREWYR PEq M I C P O C U R I E / I S P U C ~ E M I 1

WP STE ( b r 4 3 l . W R I T E 125.451 WRITE 125r45J W R I T E ( 2 6 1 10)

WR!TE ( 2 6 . 5 0 1 W R I T E 126r461 W P I T E I 2 O r 4 7 ) WRITE 127.101 WRITE 121.43) W R I T E l Z T r 5 O I

W R I T E 126.491

W R I T E 123.60t W R I T E (27.61) I F (NTYPE .NE.

C C ELECTPGN 00SE-RATE C

O J GO TO 99

FACT7)RS FOR D I F F E P E N T D E P T H S I N S K I N

i I 0 0 0 20 0

19; -rf _-

C A I P I M M E R S I O N C

7 W R I T E (18.101 W P I T E ( 1 8 r 5 1 1

5 1 FORMAT I I H O . Z X . 6 9 H E L E C T C U i POSE-PATE PACTORS FOa % ! ? 8 FCO 1 ' 4 H E D S Z I O N I N C O N T A W I N A T E 0 A I R 1

Y R I T E 118.421 W R I T E ( 1 8 . 5 2 1

5 2 F O D H A T ( L H O , 37X. (IHDEPTH OF, LOX. ~ H O E P T H OF. L O X . 8 H D E P l H O C .

Z I O X . 8HDEVTH DFI, W R I T E (18 .531

5 3 FORMAT I l H 5 X e T H N U C L I O E . 8x9 9 H H A L f - L I F E . 6X. l Z H 4 M G l l S 3 C q l i 2 6 X e l Z H 8 M G / ( S O CM1, 5X. 13H4O M C I ( S 0 C H I . 6 X t 1 Z H T M G l ( S 0 C q l l l

C C WATEP I M P E R S I O N C

W R I T E (23. 101 W R I T E (23.r 541

5 6 FORMAT ( I H O . ZX . T L H E L E C T R ( N DOSE-RATE F A C T O P S FOP S K I N FCR I ' 4 M E O S Z I O N I N C O N T A M I N A T @ D W A T E P I

WRITE ( 2 3 . 4 2 ) WP.!TE (23.521 W R I T E 123r531

C C CRCUNO SURFPCE E X P C S W E C

W R I T E (281101 W R I T E ( 2 8 , 5 5 1

5 5 FOPMAT lIHO* 2X. B I H E L E C T R O i OOSE-RATE F A C T O R S FOR S K I N FOR EXPOSU ZRE I M A6OVE C W T A H I N A T E D GROUtlD SURFACE1

ua I iE (28,501 U P I T E I 2 8 e 5 2 1 W R I T E 128.531 I F I N T Y P E .NE. 01 M TO 99

C C DOSE-P.ATE FACTORS FOR S K I N FOR PHOTJNS, ELECTRONS. A N 0 PHOTONS P L U S ELECTROYS C C A I R I M M E R S I O N C

8 W R I T E (19*10# WPITE (19.651

6 5 FORMbT I I H O I 2X. 6OHDDSE-RATE FACTORS FOR S K I N FOR I M W E P S I O Y I N CO Z N T A W I N A T E D A I P I

WP.ITE 4 19.421 WRITE (19.66) FORMAT ( I H O I 5 X r S B H V A L U E S F O R ELECTRONS CG?RESPDYO TO A DEPTM OF

W P I f E 119.671 2 7 *C/ISO C H I 1

6 7 F O R H A T ( I H O v 5 X e I W U C L I O E * 8X. 9 H H A L F - L I F E . 9x1 6HPHOTON. I l X . 2 BHELE CTROH. /I ZX. 5 H T O f A L / )

C C U A T E R 1 M M E R f I O N C

W I T € ( 2 4 , 1 0 1 WRITE ( L 4 . 6 8 1

6 8 FORMA' ( L H O t 2 X . 6 2 H O O S E d A T E FACTORS FOP S K I N FOP IMMERSIO' I I?! CO Z N T A M l N A T E O WATERI

WRITE (249421 W R I T E (24.661

198

WRITE ( 2 6 e b l ) C C CPOUND SUPFACE EXPOSUPE C

W @ I T E (29.101 WP.1TE 429.691

C 9 FORMAT ( IHO. 2 X e ? W O O ZOVE C O N T A M l N A T E D CROUN

W R I T E ( 2 9 e M l WRITE (29.661 W R I T E (29~671

E-RATE CACTC’PS FOR SURF ACE 8

I F ( N T Y P E .NE. 01 CO TO 99 C C E F F E C T I V E DOSE-P.ATE FACTORS FOR A l p . I M Y E R S I O N C SURFACE EXPOSURE C

S K I N FO1 EXPOSURE 1 M A 8

WATER f m E R S l O Y e AND C p O U N 3

9 W R I T E ( 3 0 e 1 0 8 W R I T E ( 3 0 ~ 3 2 )

32 FORMAT (LHOe 2 X e S W E F F E C T I V E DOSE-RATE FACTORS FOU PHOTONS PLUS E 2 L E C TROhS I

U R l T E (30.231 33 F O R M 4 1 tlW 9 5X. 67HIN WREMiYP. PER M I C R O C U R I E / ( C U B I C )11 FOR .UP AN

2 0 WATER I C I W E R S I J N bNDl W R I T E ( 3 0 e 3 4 1

34 F O R M A T ( I H e S X e 64HlN W R E W Y P PER MICROCUP.!E/(SOUAPE M I F B ZROUN ZD S U a F A C E EXPOSURE!

U P ItE ( 3 0 s 358

W R I T E (30e36J 3 5 F O R M A T (1180 e 39x1 3 H A I R e 14x1 SHWATERI 13x1 6”;ROIMDI

36 F O R M A T I I H e 5x1 7 W U C L I O E e 8Xe S H H A L F - L I F E e 7X. 9HIHWEP.SIOYe 9 x 9 2 9 H I H 9 E R S I O N e lOXe T H S U P F A C E / l

99 R E T U R N EN0

.

\

199

C S U 8 P . O U T I N E D I T I N ( N O U I T J

C C REAOS I N P U T OATA FOR EACH NUCLSDE C C - NQUIT - AN INDEX T O DETECT E B D - O F - F I L E FOLLOWING D A T A FOR LAST Y l K L I C E C - 0 ! N I T l A L L Y C 1 A T E N O - O F - F I L E C

OIMENSION E A L F t Z S I t F A L F l Z 5 1 s E B M A X ( 5 0 I . E B A V C I 5 0 l . F B E T 4 ( 501. 2 E p H A X t Z O I . E P A V C ( 2 O t . F P O S t Z O I t E E L E C l 1 2 5 I r F E L E C ( L Z 5 1 . 3 EGAWt ZOO1 s F C H ( 2001 OIMENSIGN t N U C L [ t ) . T k i A L F ( 3 J t N B F ( 5 ) . N P c l 5 ) COMMCNI 8 L K l / 1 N U C L s T H A L F COHMON/ B L K Z / ATNO. NFB. NBF. NFP. N P F COKHON/ B L S 3 1 N B E T A t N P O S t N E L E C t NCAH C O W M C N ~ 0 L % t E6HA%. E B A V G t FBETA. E P H A X t EPLVC. F P O S ; E E L E C t

2 F E L E C s €GAM. FC*M C C R A D I O N U C L I O E NAVE, HALF-LIFE9 WD ATOMIC NUnBER C

RELO ( 5 . 3 s E N C = 9 9 1 INUCL. T H A L F s ATNO 3 FOR.*&T l 2 A 4 r 2 X s 3A4. 3 Y s F 5 - ? !

C C NUMBER OF ALPHA P A R T I C L E S ( L I M I T rJF 231: ALPHA E K E R G I E S A M ) I N T E N S I T I E S C READ I N . I W T ARE NOT U S E D IN THE PP.OCRL.# C

R E A 0 ( 5 . 4 1 N A L F 4 FGRHAT i f 1 4 8

I F (N'LF -EO. 0 ) GO TO 9 r C ALPHA E N E R G I E S I N F E Y A N 0 I N T E H S I T I E S I N NUrCER PER D E C A Y

OF F I R S T - F O X @ I D O E N U i I O U E F IR ST-60.26 I m E N UNI WE

E BETA E N O P O I N T AND W E R A G E E t J E R C I E S I N HEY 4YO I I 4 T E N S I T I E S IN YU*8ER PEQ OECPY C

C C NUFSER 3 P O S I T R O N S I L I N l T O F 201. 'IU*OER OF F I R S T - F O I B I D O E N UHIOUE C T R A N S I T I G C S ( L I M I T 3F 5 1 9 A N 0 I tJDEX FOR EACH c I P S T - F a B 1 0 3 E N U K I G I E C T R A N S I f I C H C

R E A D ( 5 . 6 1 ( E B H A X I J I . E B A V G I J l s F B E T A ( J l s J = l s t l B E T A 1

5 R E A D I 5 t 4 l W O S r NFPs t N P F ( 1 ) . I - l . N F P J I F I N P O S .EO. 01 GO TO 7

C C P O S I T R C N E H O P O I N T A N @ A V E R A G E EYERGIES IN M E V U f O I N T E N S I T I E S IN Y W B E P PCP

. .. ___.e- - . . '

. .

200

c CECAY C

C C NUH8ER OF AUGEP A N D I N T E R N A L C C N V E P S I O N E L E C T P O N S l L ! r l T OF 1 2 S l C

R E A D (5 .61 I E P W A X I J ) . E P A V G I J I , F P O S I J I . J = l * N P O S l . .

I R E A D ( 5 - 4 1 N E L E C I F I N E L E C ,EO. 01 60 TO 8

C C AUGER A N 0 I N T E R N A L CONVERSION ELECTRON E N E R G I E S I N HEV A N 0 I N T E & ! f I T I E S I N c NUMBER PER DECAY C

C C NUWaER OF PnOTOM 1 L I M I T OF 2001 C

R E A D 15-68 I E E L C C l J I . F E L E C l J I r J = I e N E L E C f

8 R E A D 1 5 - 4 1 NCAW I F ( N c h f l .EO. 01 GO TO I

C c PHOTON EriEnciEs IN MEV ANO INTENSIT~ES IN NUMBER PER D E C A Y C

READ ( 5 . b ) 1 E G M t J1- F C A M I JI- J= l * N G A H I GO TO 1

99 NOUlT-I I R E T U R N

EM)

I

6294 201

C

C C UEITES I N P U T D A T A FOR EACH N U C L I D E C

SUBROUTINE OATOUT

OIMENSIOY E B M A X t S O l e E B A V C ( S 0 I s F B E T A I S O t * EPMAXIZO@* E P A V C ( Z 0 I . 2 ppns(zo i . E E L E C I IZSI . FELEC~IZS~. EGAM~ZOOI. F C A * ( Z O O ~

OI'EKSIOH I M J C L ( Z I * T H A L F l 3 l COMRON/ 9 L K l l I N U C L o THALF C 5 * M O N / B L K 3 1 NBETA. NPOSI NELEC. NGAM COMMON/ BLK*/ EBMAX. EBAVC. FBETA. EPMAX. EPAVG. FPOS. € E L K *

2 FELEC. €GAM* %AM C C MAXIMUM NUM9ER OF L I N E S PER PAGE FOR E A C H T Y P E O F OAT4 T A 0 L E C

C

C C TEST FOR CIP.ST T l M E THlOUGCi SUBRCUTlNE C

C c I t t I T l A L I L € L I N E COUNT FOR EACH TABLE; RESET L O G I C A L V 4 R I A C t E C

O A T A N U L I O / S I / * M U L S P / S Z /

LOGICAL S I R S T / .TCUE. /

IC (.NOT* F I R S T I GO TO 9

L I N I O = O L I N B E T = O L I N P O S - 0 L1 N E L - 0 LINGAM-0 F I R ST-.FALSE.

C C RADIONUCL!OE AN0 SPECTRAL I O E - N T I F ! C A T I C H C

9 IO

I1 C C B E T I - P & R T l C L E OATA C

C A L L D I T L I N (NBETAr i B M A X ( 1 I o E B A V C ( l J * F B E T A l l J . LINBETm MAXLSP.

I F ( N B E T I -EO. 1 1 GQ TO 12 00 ! z J-ZrPZlETA

2 l o 11. 29

CALL 0 4 T L I N t t : E T A * E B M C X I J I . E B A V G t J l r F d E T A l Jl, L l N B E T r RLXLSPI 2 Jo 11- 21

15 C O N T I N U E 12 I F I H P O S .EO. 01 GO TO 18

C C POSITRON DATA C

000205

202

i

203

. . C

S U B R O U T I N E O A T L I N I N D A R T S EMAX. EAVG. F I N T . L I N E S W A X L I N e NL1’4€. \ ‘ 2 N P R l N T t N T Y P E I

C C YRZTES E A C H L I N E O F B E T A - P A R T I C L E S P O S I T P O N S AUGER AN0 I N T E P N A L C O W € P S I O U C C C C C C C C C C C C

C

ELECTRON. OR PHOTON OATA

N P A R T - WtlBER OF SPECTRAL L I N E S 3 F P A R T I C U L A R 9 A 0 1 & l I O N TYPE E M X - E N D P O I N T ENERGY OF P A P T I C U L A R S P E C T P A L L I N E E A V G - AVERAGE ENERGY @F P A R T I C U L A R SPECTRAL L l N E PINT - I N T E N S I T Y O F PAP. f fCULAR S P E C T R A L L I N E L I N E - L I N E C(Y:NT FOR OATA T A B L E FOP P A R T I C U L A P . S P E C P A L L I N E W X L I N - MAXIMUM L I N E COUNT FOR OATA T A B L E FOR P A R T I C U L A R R A O l A T l O H TVDE W I N E - I N D E X FOP SPECTRAL LINE OF P A R T I C U L A R R A O I A T I O N TYPE N P R l W T - OUTPUT O E V I C E NUMBEP N T Y P E - I N D E X FOR R A D I A T I O i l TYPE (SEE S U B R O U T I N E P R I W FOR LISTING1

D I M E N S I O N I N U C L ( 2 J e T H A L F O I CflMMOFI/ B L K I / I N U C L e T H A L F

c T E S T FOR F I R S T S P E C T R A L L I N E OF P A R T I C U L A R R A O I A T I O N T Y P E C

C I F I N L I N E -NE. 1 ) GO TO 1

c WITE F I R S T SPECTRAL ’LINE ’

C C C

C C C

C C C

C

TEST FtR C O N T I N U W S OR O I S C R E T E R A O I A T I O r (

IF (EMAX .EO. E A V G I GO TO 2

B E T A - P A I T I C L E CR P O S I T R O N DATA

U P I TE 4 NPR INf. 31

GO TO 4 3 FORRA: 1 1 H O . +X.

AUGER AN0 I N T E R N A L

2 WRITE I H P U I N l e 5 1 5 F O R W I T I l H O e 4 X e + L I N E - L I N E * Z

GO TO 6

C O N V E R S I O N E L E C T R O N OR PHOTON O A T A

I M J C L . THLLFe EMAX. F I N 1 LA49 5 X e 3 A 4 e 7X. F 7 . 4 ~ 9%. F8.5)

C W R I T E f E C O 3 0 A h 9 SUBSEOUENT SPECTRAL L I N E S U S I W SAME PUOCEOUOE AS A C

L I F (EMAX .EO. E A V G I GO TO 7 W R I T E I N 3 R I H T e B l EMAX. E A V C . F I Y T

GO TO 9 a FORHAT t i n e 3 6 ~ . t 1 ~ 7 . 4 . 9x1. F8.s)

7 WP.11E I N D R I N T . l O l EWAXe FIM 10 FORMkT ( In e 3 6 P e 67.6s O X e FB.51 9 L I N E - L I N E 6 1

C C T E S T F O R EN0 OF P A G E C

; . . ; . , 000207

9 0 V E

/ 204

6 I F (LINE .LT. WAXLINI GO 10 11 C c Y R I T E T A 8 L E HEAOINCS ON NEW PAGE AND SKIP A L I N E AFTEI HEAOINGS c .

CALL PRINT (NTYPEI LINE-0 IF IHLINE 60- 1 -AND. NPART ONE. 1, W I T € ( N P P I N T r l 3 8

13 FORMAT I l M t I F IHLXNE .ME. 1 . N O . NLINE .WE. NPARTI URRITE (NPRINTe13l

11 RETURN END

J

205

C

C C C A L C U L A T E S DOSE-RATE CONVERSION FACTORS FOn EXTERNAL E X P O S W E 10 PHOTONS A N 0 C LLECTRONS C

SUBROUTINE CALC

O l M E N S l O N E B M A X ( 5 0 1 . EBAVC(50l e F B E T A t 501. E P R A X I Z O I s E P A V C I 20 1.

D I M E N S I O N N B F t 5 1 e W F I S I OIWENSXOTI € 9 1 2 5 1 . F M U E A R I Z S l r F *UEHRl258e F ~ V F T R I Z ~ I ~ F M U A R ( Z 5 I .

2 F P O S l Z O 8 . EELECI k25I. F E L E C l l 2 5 l r E C M 4 2 O O l * F C A Y l 2 0 0 )

2 S P A R l 2 5 1 e SPWR(Z5). S P T R ( 2 5 J r R N A R l 2 S 1 R N T R ( 2 S b e C A R 1 2 5 1 3 O A R 1 2 5 1

O l M E N S I O N E A R I B I * I I I P H A P I B I ~ E A P L I 819 R S K N I 6 8 . P A 4 4 1 e EWAY(C8.

O I W E N S I O N CfAR(251e GfYRl2S)r B T A R f Z S I e B T y I ( 2 5 l O I M E N S I O N E B S R l l i O l ) . RTARtbOOJ. R T N R t 6 0 0 l * A L R ( 6 O O 8 e F I E 1 6 0 0 8 01 M E N S I O N SGAORG4 2 31 SGUORG(Z3 1 e SCGUZCt 23) * S81ISKN14 8 v

0 1 ME143 ION O I M E N S I C N 00SORG!3.238e M S O R a l 3 . 4 ) . W f S K N I 3 l O O S E F F ( 3 t OlMENSION O E F F l 3 r l S ) r O E F F S O e 1 5 1 . O U M l ~ l S I e DUM21 151 COMMON/ I L K Z / ATNU. HFB. NOFe NFPI NPS C O W O N / BLU3/ N B E I b t HPOSr NELECe NGAM COMRON/ B L X W €€MAX* E3AVG. FBETAe EPMAXe EPAVC. F p O S r E E l E C e

2 EMGR441. C P M l 6 l

2 SBWSKNtClr S B C Z K N l 4 l ORGF ACt 2 3 I * GF AC 1 6 9 e 00 1

2 F E L E C e ECPMD FGdM . COMMOt4f ELKS/ DOSCRCe OOSCRB. DOSSKh. OOSEFF

OOUBLE P i i E C I S I W E l C

C A T T E N U A T I Q Y CGEFP:CIEN?S* BUILY’JP FACTOR PARAKETERS. A N 0 ORGAH DOSE-RATE c tmttiEs SCR R P E a E w x VUUES s PHOTON ENERGY-ABSOPPTION COEFFICIENTS.

C TASTORS: AH0 ELECTRON STOPPIPS POUFPS AN0 RPKGZS-VALUES I N HEV C

OATA ER/ 2 0.060.

4 4.0. . 3 O.SooD

C C R E F E R E X E VALUES C (SO C K I / G C

. D A T A FF?UCAR/ 2 0.03051 3 0.0296r 4 O.Ol6G.

C C REFERENCE VALUES c (SO C#IIG C

D A T A FWJEYRI 2 0.03201 3 0.0330. 4 O.023be

C C REFERENCE VCLUES

0.0k01 0.0151 0.020. 0.033e OoOCOe 0.050e 0.0801 0.100. 0.150e 0.260e 0.300. 0.6008 0.6aa. 0. eoo. I . 0 e 1.5. 2.0.. 3.0 .

5.0, 6.0. 6.0. lO.C/

O F PH0T;)rr WAS5 ENERGY-ABSORPTION C O E F F I C I E N T S I N A!N IN

4 . 1 9 e 1.28r 0.512e 5.149. 0.0677. 0.0*?8* 0.0242, 0.0256r O . O t t t * 0.0297. 0.0319. 0-0328r 0.0325. 0.0321r 0.0309. 0 0 0 2 8 2 1 0.0260* 0.0127. 0 - 0 1 9 L e 0.0180* 0.0146. 0.0157/

O F PHCTOn MASS ENERGY-ABSORPTION W E F F I C I E N T S 11. T I S S U E C ( H U S C L E I I N IS0 WJ/C

206

C O A T A FRUETW 4.87. 1.32. 0.533. 0.156. O.OTOI. 0.0~31.

3 0.032e. 0 . 0 3 ~ 5 . 0.0318. 0.0308. 0.0282. 0 . ~ 2 5 9 . 0 . 0 2 2 t . 4 0.0203. 0.0168. o.oire. 0.0163. o,o154/

2 0.0328. 0 .0264. 0 .0258. 0 . 0 2 7 5 . 0.0296. 0.0317. 0.0325-

C C REFESENCE VALUES OF PHOTON MASS A T T E N U A T I O N COFFFICIEYTS IN A l a IN C I S 0 C M I / G C

DATA F W A R / 4.99. 1.55* O . 7 5 2 r 0.349. 9.248. 0 .208. 2 0.188. 0.!67* 0 .154. 0 . 1 3 6 . 0.123. 0.107. 0.0954. 3 0.0810. 0.0805. 0.0707* 010636r 0-0518. 0.0445. 0.0358s 4 0.0300. O.Oi75i 0 . 0 2 5 2 , 0.0223. 0.020* /

C C REFERENCE VALUES O F PHOTON T I S S U E - T O - A I R OOSE P A T 1 0 FOR I M M E R S I O N I N C C Q N T P M I N A T E D AIR: VALUES ARE R A T I O OF MASS E H E Q G ~ - A 0 5 C I R P T l D W C O E F F I C I E W T S c AVERAGED OVER SPECTRUM OF Pnmcms IN AIR FROM MONOENERGE'IC S O W ~ C E S AND AQE C O B T A I N E D FROM F I G . 6 OF D I L L M A N I 3 E A L T H P H Y S I C S 279 571 (19741 C

OATA C f A P l 0.954. 0.954. 0.956. 0 -961r 0.973. 0.985. 2 0.998. L O I B I 1.032. 1 ~ 0 5 4 t 1-066. 1.078. 1.085. J 1.089. 1.091. 1.094. 1.096. 1-099. 1.101). 1.098. 4 1.094. 1.090. 1.085. 1.076. 1,067/

C C REFEPENCE VALUES OF ELECTRON MASS STOf'?INC POWERS I N A I P I N ( *EV-SO C M I l G C

OATA S?hR/ 19.7. 14.4- 11.69 8 - 6 8 , h.84. 5 . 8 1 ~ 2 3.11. 4-2Oe 3-63. 2.86. 2-41, 2-09. 1-91. 3 1.811 1.75. 1.10r 1 -68 . 1-60. L - 7 1 * 1-19. 4 1-85, 1-91.. 1-97, 2.07. 2.16/

C c P E F E R E N C E VALUES OF ELECTRON MASS S T O P P I N G POWERS I N WATER IN (MEV-S@ C W I I G t

4 1.97, 2 . O l r 2.05, 2.12, 2-18/ C C REFERENCE VALUES OF ELECTRON MASS S T C P P I N G P0HEP.S IN 1 C tMEV-SO CM1/G

' C OATA S P T R I 22.9, I6.7t I304r 9-11.

2 5.86. 4.80r 4.15. 3-27, 2-82, 3 2.05. 1.9Sr 1.92. 1.891 1-89. 4 2 - 0 6 . 2.13, 2.18. i . 2 8 , 2.37 /

C C REFERENCE VALUES OF ELECTRON RANGES I N A I R I N G / ( S O C H I C

SSUE MUSCLE1

I

OATA ANAPf 2.89E-4. 5-90E-4, 9.81E-4, 2.OlE-3. 3.33E-3. 6.9ZE-3. 2 6-?6E-3* 0.0111* 0,0163. 0 - 0 3 2 0 * 0.0509. 0.09541 0.146. 3 0 - 2 0 0 * 0.256. 0-372* 0.L91. 0.199. 1-08r 1.M- 4 2-21. 2.14. 3.25. C-26. 5.191

C C FEFERENCE VALUES OF ELECTP.CN PCYGES I N T I S S U E (M'JSCLEI IN W I S O C ' 4 I C

D A T A R N T Q 1 2.47E-4. 5.06E-41 8.4iE-4. l.72E-3. 2. e8E-3. 4.27E-3. 2 5.87E-3. 9.S7E-5. 0.0142. 0-0219. 0.0445. 0 .0836. 0.126. 3 0.175* 0 . 2 2 5 . 0 . 3 2 8 . 0.433. 0.698. 0.960* 1 - 4 1 . 4 1-961 2-44, 2-91. 3 . 8 0 1 . 4 . 6 t I

N

6294- . r i

207

C C C C

C C C C

C C C

C C C C C

C C C C C

C C C C

C C C C C

C

C C C

C C C

t c C

REFEPENCE VALUES OF 6 E R C E R euILoup FACTORS IN AIR

O A T A CAR/ 0 . 3 3 3 0 . z 4 - 2 0 . 4.469 3 1 - 6 8 . 1 .53 . 4 0.602. 0 . 5 4 6 .

C AN0 0 C O E F F I C I E Y T S FOK P'4OTGN E P ! E P t Y - A 6 S C V P + l O u

D A T A OAR/ -0.Ob601 -0.0b93. -0.0b07. -0.0230q 0.0264. 0 . 0 7 4 3 . z 0.106. O . l S l r 0 ) r l b E e 0.178. 0 . 1 7 2 . 0 . 1 4 2 , 0.125. 3 0 . 1 0 6 . 0 .0946. 0.0145m 0.0104. 0.03T3. 0.02421 0 . 0 1 0 0 r 4 0 . 0 0 3 2 . -0 .0012~ -0.00291 -0 .0035r -0.0033/

E N E R G I E S FOP REFERENCE VALUES OF ELECTRON S C A L I N G PAR4WETER * A L P H a * F 9 P A I R JMWERSION

D A T A EAR/ 0.0101 0.02Oi 0.050. 0.100. O - Z G J . O-SOOm 1.0. 2 2-01

REFERENCE VALUE5 O F ELECTRON S C A L I N G PARAMETER * A L P H A * FOR A I D Im€RSI ON

D A T A A L P H A U I 1.3221 1.016. 1.016r 1.016. 1.OlTs 1 . 0 1 6 . 1.009. z 0 . 9 9 2 /

FACTOR TO CONVERT A6SORBED EKEPGY I N N E V TO DOSE E W I V A L E N T !N PEW IN

NUMBER 0; SECONDS PER YEAR 1 G-R EM I /NEV

D A T A F K r FS/ I .60206E-09. 3.153bE*O7/

O E N S I T Y W DRY A I P A? 20 OEG C AND 750 NM PRESSURE IN C I I C U C n l OENSITY' OF 3ATER AT 20 DEG C IN W t C U CM@ H E I G H T OF REFERENCE P O S I T I O N FIR GSOUNO SURFACE EXPOSURE IN CW

D A T A RMOAI RHOMI L/ 1 . 1 6 9 E 4 3 . 0 .99623. 101.0/

DEPTHS OF S K I N eELw e m SURF=€ AT YWICH ELECTRON DOSE-RATE F A C T ~ R S ARE C A L C U L A T E 0 IN W t S O CMI

D A T A R S K W 4.OE-3. B.OE-3. 4 .0E-Zr t .Oi -31

P A R T I C L E - M E D I U M DOSE-RATE C D R R R T I O n F A C T W S : OROEP IS PHOTON O O S E 4 A T E CORRECTION FACTOR FOB A I R IMMERSIOWr WATER SHNERSIOY. AND C P o U h U SUPGACE EXPOSUREr AND ELECTRON DOSE-RAVE CORRECTION FACT- FOP TliREE EXPOSURE MOOES

DATA C P W 0.5. 2.1.0. 3.0.5/

L U G I C L I L F I R S T / .TRUE./

TEST FOR F I R S T T I M E THROUGd SUWOVIINE

IF (.NOT- F I P S T I GO TO 19

C A L C U L A T E REFEOENCE VALUES OF P A T I O S OF PHOTON MASS EYEPCY-A6SORP113N C O E F F I C I E N T S IN T I S S U E 70 VALUES I N WATEP A N 0 ELECTRON MASS STODPING POdESS I N T I S S U E TO VALUES I N A I R APID WATER AT E N E P G I E S G I V E N 8 Y VALUES OF EP

DO 20 I - l r 2 S G T Y R ~ I ~ - ~ ~ U E T R ~ I ~ / ~ M U E ~ R ~ I l

.: - " , . /

208

e l m ( I I - S P T R ( I ) I S P A R ( i I BTWRlI l = S P f R I I l / S P U R ( I l

20 CONTINUC C C C:.'.CULATE CONSTANT FACTOPS I N W S E - R A T E FACTOR EQUATIONS TO G I V E OUTP?IT 1'4 C OESIREC U N I T S C

FAC1=37.*FS f K F A C 2 - 3700. *FS *FK

C C C A L C U L A T E H E l G b f f OF REFERENCE W S I T 1 0 ? 1 FOR G R O W 0 SUaFACE EXPOSURE I N

C

C C C A L C U L A T E N I N I N J W ELECTRON ENERGIES C D N T R I B U T I ? t G TO 00SE-RATE F A C T m S FOR S K I Y C FOR D I F F E R E N T OEPTHS BELOW B W Y SURFACE C C A I R AN0 MATER IMMERSION C

c w t s a CMI

R-RHOA*Z

00 61 I - I r 4 ERAWlI~~YIHTEP.lRSKH~IIr RNTRr E R r O r 3. 251

6 1 C O N T I H U E C C CRWND SURFACE EXPOSURE: C A L C U L A T I O S S ASSUME THAT THICKNESS OF T I S S U E I f C REPLACED BY EOUIVALENT THICKNESS OF A I R C

00 62 1-1.4

E W C R ( I t = Y I N T E R ( R A 1 I 4 r RNARr ER, 0 . 3. 251 R A ( Il=R*RSW(I 1.1.14

62 C O N T i N U E C C D E F I N E ENERGIES FOR CALCULATI t IG 3;ECTRUM FOR B E T A P A R T I C L E OR POSI TROV--V4L9ES C ARE EVERY 10 KEV FROM 0 TO 12 MEV C

E B S R ( I l r O . 0 00 39 I - Z * 1201 EBSR~l~-EBSR(I-ll~O.OlO

39 C O ~ T I r l U E C C A T ENERGIES G I V E N BY ALTERNATE VALUES O F EBSRr CALCULLTE R A T I O S OF ELECTa5N C M A S S STOPPIk! ! COYER I N T I S S U E TO V B L U E S I N A I R AH0 Y A T E q r VALUE OF ELECTRON C S C A L I N G P A R i l i E T E R *ALPFra r AN0 GEOMETRICAL R E O U T I O N FACTD9.S FOR E L E C T R 9 N C DOSE-RATE FACYCRS FOR 0 I F F E R C N T i C E P T H . S BELOW $COY SURFACE FOR A I R AN0 Y 4 T E R C I M M E R S I O N C C C A L C U L A T E LOGARITHM OF HEFEREIdCE ENEO.GIES FOR E L E C T R W SCALSNG PAPA*ETES C

DO 63 1-l .a E A R L 1 I l = A L O C ( E A R t I I I

6 3 C O N T I N U E 00 6 4 J=Z* 1200.2 U = J f 2

c, C C A L C U L A T E R A T I O S OF ELECTRON MASS STOPPING POUER It1 T I S S U E TO VALUES I N A I R C A N 0 WATER C

R T A R l K l r Y I N T E R ( E 8 S R l J ) . E R r B T A R r O r 3. 251 R T Y R l K ~ ~ Y ~ N T E R I E 8 S R l ~ l r E R r BTWRr O r 3r 251

._ - .I

209

6294- - . 4 3 -

C C C A L C U L A T E ELECTRON S C A L I N G PAP.AMETER * A L P H A * C

C C C A L C U L A T E ELECTRON GEO?4ETRICAt P E O W T I O N FACTORS FOX O I i F E P E N T 3 E D T I ( S OELTJb C 6OOY SURFACE FOR A I R AN0 YATER IMir€RSION; R E S E l L O G I C A L V A R I A f J L E C

A : R t K ) = Y l N T E o ( A L O C ( E S ~ R t J ~ ~ s E IRL. ALPMAR. 0. 3s 8 )

00 45 l = l e 4 I F I E B S R I J ) . G E . E M A W I I J ) GO TO 66 C F A C t I mK3=O.O GO TO b5

6 5 C O N T I N U E 64 C O N T I N U E

66 G F A C t I . K I ~ C l R S R N l I I * RNTP.. E9SP.l J l I

F I I S T - . F A L S E - C C I N I f l A L I L E SUM#AT10( TERMS I N M)SE-RATE FACTOR E Q U A T I O N S C C PnOTo)4 DOSE-RATE FACTORS FOR BODY ORGANS FOR THnEE E X P O S W E M@@ES C

19 00 1 Jsls23 SC AORCI J I -3. 0 SGwORGtJI-0.0 SCGURGIJI-0.0

1 C O N T I N U E C C E L E C T R C N DOSE-RATE FACTORS FOX S K I N FOR THREE EXPOSURE M m E S C

00 38 J l l r 4 S B A S K N t J I -0.3 SB K S W ( J I -0.0 SBGSXNtJI-0.0

38 C O # T I H U E IF (NGAW .Ea- 0 ) GO TO 2

C C C A L C U L A T E SUMMATION TERMS I N PHOTON OOSE-RATE FACTUR EOUASIONS C

C C C A L C U L A T E RATIOS OF MASS El4ERGY-48SORPf ION C O E F F I C I E N T S IN T I S S U E TO VALUES C IN A I R A N 0 WATER C

00 3 I = I * ? I C A M

R T A = Y l W T E R ( E G A S ’ I I * ER. CTLRs 0. 3 9 258 R T U ~ I l W T E R t E C A R l I ~ s ERm CTURI 0 s 3. 251

C C C C

C C C

C C C

C A L C U L A T E MASS ENERGY A 6 S O h P f I O N A N 0 MASS A T T E N U A T I O N C O E F F I C I E Y T S I N A I R IU ( 5 9 CPO/C

F H A ~ Y ! N T E R ( E G A M ( 1 1 1 ERs FRUEAR* 0 s 3. 2 5 ) ~ M A L ~ Y I N T E R I E C A M l I J m ER. CWARm 0. 3 s 251

C A L C U L A T E BERGER BUILOUP FACTOR C O E F F I C I E ‘ 4 T S C A h 9 0 i N A I R

I F (€CAM( 1 1 .GI. ER1111 CO TO 15

USE L I N E A R I N T E R P O U T I O N FW. C C O E F F I C I E N T FOR ENEP.GIES L E S S W A N IO UEV

CA-(ECAM( I J / E R I 1 J )*CAR! 11

000213

i _- . .

210

GO TO 16 15 C A ~ T I ~ J T E R l E C A M l I l ~ ER. CAR. 0. 3 r 251 16 O A ~ l l N T E R I E G A M l I l r €Re OARS Om 3 s 251

C A L C U L A T E R A T I O S OF ORGAN OOSE RATE TO DOSE R A T E I N A I R FOR A I D I M M E R S I O N

00 4 K - 1 ~ 2 3 O R G F A C ( K 1 ~ F A C I K . E C A M l I l ~

4 C O N T I N U E

C A L C U L A T E SUMMAT I O N TERMS FOR A I R I M M E R S I O N e Y A l E R I M h E R S I O N . A N 0 CROUNO SURFACE EXPOSURE

I S - F C A M I I l . E G A M l I 8 T C A - c M A * l E 1 (DELE1 F M A L I 9

DO 5 K m l . 2 3

DELE I R 1 I -1 C A / I D A - 1.0 I I *EXP t 4 011-1.0 l * F * A L * 2 R I I

SCAORCI K l - S G A O P C I K l * T S * O R C F A C l K l S G U O R C ~ K l - S C W O R G l K ~ ~ T S ~ O R C F A C l K l * R T Y / R T A S C G O R G ~ K l - S t t O R G l K 8 * T S * T C A * O ~ C F A C I K l

5 C O N T I N U E 3 CONTXNUE

C CAfi.CULATE PHOTaY OUSE-RATE FACTORS FOR E O D I OPCANS FOR A I R IWERSIW. YATEP C IMHERSIO%r AND GROUND SURFACE EXP0SUP.E C

2 OI) 6 Km1.23 OOSORCI I r K 8 - C P M l I l * F A C l * S G A O R G l K l / R H O A OOSORC ( 2 . K I * C P U l 2 )*SAC l*SCUORClU 1 / R W Y OOSORC l 3 e K 1-C. S*CPMI 31.F A C P SCMRC I K I

6 C O N T I N U E C c C A L C t l L A T E S U M M A T I O N TERMS IN ELECTRON 00SE-RATE F A C T 0 9 E O U A T 1 r V S C

C C C

C C C C C

C C C

C C C

I F ( H B E T A .EO. 01 GO TO I

BE 1 A -P LP. T I C L E f .

00 8 I ~ I ~ N O E T A I F ( E O M A X I I ) .LT. EMAY(118 GO TO 8

C A L C U L A T E XT A-P ART1 C L E SPEC TRUM

SET I N O E X FOR ALLOWED B E T A T R A N S I T I ( r t

N C O - 1

T E S T FOP. F I R S T - F O a B I D O E N U N I O J E TP.ANS1TION A N 0 R E S E T I N D E X

25

24

I F I N F B .EO. 01 GO TO 24 00 25 J- lsNFB I F ( 1 -NE. N E F t J l I 63 TO 25 N C O * - l GO TO 24 C O N T I N U E

C A L C U L A T E SPECTRUM

CALL B S P E C I E E M A X I I l e F E E T A I I I . EESR. ATNO. NCDe FIEm JSPECI E M I O I

0.00 2 14 . .

.

C C C C

C C C

C C C

C C C

C C C

C C C

C C C

C C C

\ . ' _. . \. . _

211

,.:\ 6204- -

2 9

2 8

44

43

7 a

CALCULATE RATIOS OF MASS s T c P P i r i t POWERS IN TISSUE TO VALUES IN A I D AYO WATER FOR C:IEQGY INTERVAL CONTAINING ENDPOINT ENEPGY

R T A * Y I N T E R I E H I O . E R r ETARr O r 3. 2 5 1 R T Y ~ Y l N T E R ( E M I 0 r ERr BTWR, O r 3r 2 5 1

A I R IMMERSION W D YATER IMMERLION FOR OIFFERENT DEPTHS BELOW BODY SURSACE

00 28 L11.4 I F ( E 9 M A X l I l .LT. E M A W t L l I GO TO 2 8

CONTRIBUTIONS FROn ENERGY INTEf iVALS CENTERED AT ALTERNATE VALUES OF EBS3

00 29 P Z r J S p E C . 2 I F IEBSRIJI .LT. E M A Y I L I I 0 TO 29

TA*F I E : K l *EBSR I J IoRTAR t K I-CFAC I L r K I /ALP (K I TU-F I € ( K I * EBSP ( J I *PTWR (K l *GFdC I L r K 1

K - J I 2

S B A S K N l L l = S a 4 S R N I L I * ~ A SOWSKN ( L I =SEWS KN 1 L J *TU CONTINUE

CONTRIBUTION FROM ENERGY I N f E R V d L CONTAINING ENDPOINT ENERGY

ALENO~YINTER(ALM;IEM10I~ EARL# ALPHAR. O r 3. 81 C E N O * C I R S R N ( L I r RNTRr E N I D 1 T A - F I E ( K * L I * E # ID*QTboGENO/ALENO TU-F IECK+L I *EM IOUITY*CEND SBASRNt L) =SBASKN(L! +TA S B Y S K N ~ L ~ - S 6 Y S K N l L l ~ ~ ~ CON?INUE

GROUND SURFACE EXPCSUZE FOR DIFFERENT DEPTHS BELOW BODY SURFACE

00 43 L.114 I F (EBWAXIII .LT. EMGRIL#I GO TO 43

COWTRI8UTIONS F R W ENERGY INTERVALS CENTERED AT ALTERNATE V I WES DF EBS9

00 44 J l t r J S P E C r Z I F (EBSRtJB .LT. EHGRILI) CO 10 44

C A L L BCflND I E E S R I J l r RNARr R A I L ( . RANGE* E I N T I K - U 2

TC-F IE IK#*EBSR t J I .P fARlK 1 - E I N T l R L X C E SBGSANI L l = S B G S K N l L I * T G CONT I N U E

CONTPIBUTION FROM ENERG* INTERVAL C m T A I N I N C ENDPOINT ENERGY

C A L L BCKNO (EMID. RNARr R A I L I r RANGE* E I t ! l I l G - ~ I E ~ K * L l * E M I O ~ R T A a E I H f / R I N T ~ R A N G € SBGSKNI L l - SBCSKN(1 I .TG C O N 1 I NU€ CONTINUE I F (NPOS .EO. 01 GO TO 10

POS I TRONS

212

I

C C C C

DO C1 1 - I r N P O S I F ( E P M A X ( I 1 o L T . W A d l l ) ) GO TO 11

C A L C U L A T E POSITRON SPECTRUM

SET INDEX FOR ALLOYED POSITRON T R A N S I T I O N

NCD-2

T E S T FOR FIP.ST-FOR0IDDEN U N l W E T R A N S I T I O N AND RESET IMEx

I F 1 N F P .EO. 01 GO TO 67 00 68 J- l rNFP I F ( 1 -NE. N P F t J I I CO TO 68 N C D I - 2 GO TO 67

68 C O N T I N U E C C C A L C U L A T E SPECTRUU C

67 C A L L BSPEC ( E P W X t I t . F P O S 1 l I r EBSRI ATNO* NCDr EIE. J S P E C r €*IO) C C C C

C C C

c . C C

1 5 C C C

C A L C U L A T E RATIOS OF MASS STOPPING POWEdS I N T I S S U E TO V A L U E S I N A I D AVO WATER FOR ENERGY I N T E R V A L CONTAINSNG ENOPOIHT ENERGY

R ? A = V I N T E R ( E M I D r ER. B T A R r O r 3r 251 R T Y I Y I N T E R 1 E W I D r ERe BTWRr O r 3r 2 5 )

A I R I M H E R S f O ~ ~ AN0 UATE': IMHEP.S10;4 COR D I F F E R E M T DEPTHS BELOW BODY SURFACE

00 74 L11.4 I F t E P W A X ( 1 ) -11. E M A U t L J I GO TO 74

C O N T R l B U T I O N S FROM ENERGY I N T E R V A L S CENTERED A T ALTERNATE VALUES O F EBS?

74 CONTXNUE C C CROLWD SURFACE El'OSURE FOR D I F F E R E N T DEPTHS BELDY BODY SURFACE C

DO 78 L - l . 4 16 tEPMAK[II .LT. EMGRtLIl GO TO 7 8

C

000216 - .

-- .

. - - . ,

.;I.

. . .

- . . -

213

C C

C C C

C C C

C C C C

C C C

C C C

C

79

18 11 LO

. . ,

CONTRIBUTIONS FROM ENEPCY INTERVALS CENTEREO AT ALTERNATE V4LUES 0 s €959

00 79 J-2, JSPEC.2 I F t E B S R t J 1 .LT. E f f i R ( L l 1 GO TO 79 K - J l 2

TGIF I E t K I * E B S K ( J I*RTAR(K l *EINT/RANGE SBGSKNt L I - SBGSKN t L 1 TG CONT INUE

C A L L BGRNO ( E O S R ( J l r PNARI R A ~ L I I PANG€* EINTt

CONTRIBUTION FROM ENERGY INTERVAL CONTAINING ENOPOINT ENERGY

AUGER AN0 CONVERSION E L E C T W M

00 14 I = l * N E L E C I F I E E L K I I J oLT. E H A U ( l ) l GO TO 14 TS=FEL€C(l1*EE~ECIII

18

82 14

CALCULli?E R A T I O S OF 11455 STOPPING POUERS I N T ISSUE TO VALUES IN A I P AYD WATER

R t ~ ~ V ! N T E R I E E L K ~ I I ) r E R v BTARI 01 3. 251 R T ~ ~ ~ V I N T E R ( E E L K ( ! ~ I E R I 8TWRe 01 3 9 25)

A I R Im(ERSI0N AN0 WATER IRMERSION FOR OIFFERENT DEPTHS BELOW BUDY SURFACE

00 l a ~11.4 I F ( E E L E C I I J o L T - ERAY(L1) G3 TO 19 A L E N O ~ V I H f E l ( A L 0 ; I E ~ L E C ~ 11 1. EARL. ALPHARt 01 I r 81 C E N D ~ C ~ R S K N I L ~ I RNTR. EELECI I O tA=TSWWA*GERD/ALEND T l l - l S * R T W C E H D SBASKHC L) -SaASKN( L 1 +TA SBYSKH t L f =SE#SKli~L J *TU CUPtTIMlE

CRCUNO SURFACE EXPOSW.E FOR DIFFERENT DEPTHS e a o u BOOT SUPFACE

C CALCULATE ELECTRON OOSE-RATE FACTORS FOR %IN FOR DIFFERENT OEPTHS BELOW 900V C SURFACE COR A I R IMMERSION. WATER fMMERSIONv AM0 CROJNO SWFACE EXPOSURE C

1 3 00 83 Ksl .4 OOSORB: 1 K )IF ACl*SBASKN@K I /P.K)A O O S O R G ( Z ~ K t ~ f A C l ~ f ~ ~ S K N ~ K J / ~ H O Y

000217

.. .

, 214

O O S O d 8 ( 3 e K )=O. S*CPM(bI*F A C F SBGSKN(K1 e 3 CONTINUE

C C CALCULATE SUM OF PHOTON AN0 ELECTROY OOSE-DATE FACTCnS FOR S K I N F 3 P A l p C IN14ERSICNr WATER IMMERSION;. AN0 G R W Y O SURFACE EXPOSURE U S I N G VALUE AT Y E D T 4 C CF 7 WG/ISO CMJ f W ELECTPOYS C

00 59 1-1.3 OOSSMNt I J *OOSORGl1.17J *OOS(RB1 I;. 4 )

5 9 CONTIHUE C C C A L C U L r T E E F F E C T I V E DOSE-PATE FACTCQS FOR PHOTONS FOR Alp 1MMEP.SIGN;. MATE? C C C

C C C C

C C C C

C C C C

C C C

INHERSION;. AN0 CROUP40 SURFACE EXPOSURE U S I N G O P G A N - S P E C I F I C WE I f H T I N G FACTORS I N I C R P PUBLICATIOW Zb

00 26 1-1.3

C O N T f l I B U T I U N S F R O n GONADS (TESTESIr BREAST* RED MAR90d. LUNG;. f H Y n O I O * AND BONE SURFACES

00SEFf~I1~0~ZS*OOSORC~Ir20~~0~15*00SORGt1;.+~*0~12~~DOSOPtllr13~* 2 O O S O R C l I r l ~ ~ l * O ~ O P l O O S O R G l I ~ 2 2 l * W S ~ G ~ I e168t

P E O E F I N E ARRAYS CF OOSE-RATE FACTJRS F 3 R 8001 W.6IN.S TO EXCLUOE ORSANS ACREAOY CONSIOEPED PLUS OVARIES AN0 S K I N

71

5 0

5 1

00 71 J-1.3 O E F F t 1 r J ~ ~ O O S O R G ( I r J l CONTINUE 00 50 J-5110 OEFF 4 I *J-1 I*OOSORClIr J I

OEF F( I v 10 ) -00SCl lG( 1 e 12 I O E ~ F ~ I r I 1 1 ~ 0 0 S M C I I ~ 1 5 1 00 5 1 J-18.19 O E F F ( I r J - 6 ) ~ 0 0 S O R G ( I . J ) COl4TINUE O E F F I I ~ 1 4 ~ ~ O O S ~ C ~ I r Z l I O E F ~ ( 1 . 1 5 1 ~ O O S ~ G ( 1 r 2 3 1

<ONTINUE

SORT R E O E F I N E D ARRAYS OP 00SE-RATE FACTC1S FOR BODY ORGANS IN OECREASIY ' r NUMERICAL CROER U S I N C DUMMY ONE-OIWENSIONAL ARRAYS

00 52 J l I r 1 5 OUMl( J) -OEFF( I eJ1

C A L L SORT 1151 OUML. OUCIZ) 00 53 J- l r 15 O E E F S l I ; . J l ~ O U M Z C J l

52 CONTINUE

5 3 CONTXNUE

A00 C O N T R I B U T I O N S FROM F I V E @ G A M I N REHAIPIOER CATEGOPY

00 S4 J-l;.S O O S E F F t I ) = O O S E F F l I I*O.Ob*OEFF S ( I r J I

54 C O N T I N U E 26 COI4TINUE

RE TURN END

000218

215

_...

6294’: - . r i -

C

C C PERFOP-WS L b C I I A N C I A N I N T E R P O L A T l O N OF A F U N C T I O N OF ONE V A R I A B L E C C BASED ON 0OUBI.E P R R I S I O N I N T E P P O L A T I O N F U N C T I O Y YLAG OESCRl8EO I Y UNION C . C A R B I O E P U 8 L I C A T l C N C T C - 3 9 C C X I - A B C I S S A OF O E S I R E D I N T E R P O L A T I O N P O I N T C X - S I N G L Y OIMENSIONEO b R R A V O F O I S T I N C T o * O M T O N I C A L L Y I I C P E & S l f f i ABCISSAS C Y - S I N G L Y Of l4ENSIONEO A R R A Y OF C O R R E S P a O I f + G OROfhlATEf C INO? - SET TO ZERO C N l - WHBER OF P O I N T S FOR TCCE I N T E R P O L A T l O r r POLYNOMIAL C I H A X - NW48ER OF ELENENTS FOR THf X- OR Y-APRAYS

F U t l C T I O N Y I N T E R I X I . X. Y * , I N O l e N I e I M A X l

C O I W C H S I O N X l l l m 1111 I NO- I NO1 N=NL I € % - 0 IF It4 .LE. I H A X J GO TO 10 N= I MbX IEx-rt

10 I F IIHO .GT. 01 GO T O 40 00 22 J= l r [MAX IF l X I - X t J ) I 30 . 130. 20

2 0 CONTIr4UE I E X = l GO TO 7 0

30 I N O = J 40 IF l l N O .GT. 1 ) GO TO 5 0 .

IEX=-l 50 INL- I t!D-l N* 1 I / 2

I F ( I N L .GI. 01 GO TO 60 I t lL= 1

I F I I N U .LE. I M A X I GO TO BO 60 I N U - I Nl*H-L

70 I N L - I H A X - N * l I N U = I R A X

BO s=o. P-1. 00 110 J = I N L e I M J P=P. lX I -Z lJ@ t 0-1. 00 100 I - I k L * I H I I F ( I .NE. J I GO TO 90 xo=x1 GO TO 100

90 X O = X l t l 100 D=D*fXP-XIIJB 110 + S * Y t J# /D

Y I N T E R = S * P 120 RETURW 130 Y I N T E R - * I J V

GO TO 1 i C END

I

C F U N C T I m G I R s RNGTRI € 6 )

C C CALCULATES GEOMETRICAL REOUC -o( F1 C FOR A I R AN0 WATER I!WRSIO:4: SEE c 26s I :I9741 C

t

216

:OR Fm ELECTRON DOSE-RATE FACTOR FOR OS. 1151- (18J OF EERCER. H E A L T H PHIS12

t -

0 o 02 2 o

C

217

-- I.*

C C

C C C

C C C

C C

. c

C C C

C C C

C C C

C C C

C C C

ZQRNG-O.15

O A T A G U W 0 .3041 . 0 .3063 . 0 . 3013. 0.3r117. O . 3 0 8 l r 0.30311 0.3079. 2 0.3074. 0.3069. 0 .3054. 0 . 3 C r l . 0,3013. C.3002* 0 .Z987e 0.2974r 3 0.2952. 0 .2937. 0.2906. 0 . 2 8 8 l t 0.2811. 0.28b5. 0 . 2 8 6 3 . 0.2862.

‘ 4 0. t8b6. o.ie?i/ Z Q P N C 4 o Z O

D A T A GK5/ O.ZS0O. 0.2600. 0 . Z 6 1 1 e 0.2618. g.Zb?lr O . 2 6 E I . 0.26201 2 0.2t14. O.ZCO9. 0.2592. 0.2582. 0.2559. O . Z S ; S * 0 .2529. 0.2516. 3 0 .2494 . 0.24T9. 0.2449. 0 . 2 4 3 1 s 0.2418r O.241C* 0.2414r 0.2614.

0.2420. 0.24211 ( ZQRNC-0.25

Q h i h CPb1 0 .2165. 0 .2186. 0.2197. 0.22059 0.2207, 0.22001 0 . 2 2 0 7 ~ Z 0.2202. 0.2197. 0.2181. O.Zl71. 0.2150. 0.2136. 0.21221 0.2109. 3 3.2009. 0.207Te 0.2050. 0.2034. 0.2025r 0.2023. 0.2025. 0.20279 4 0.2036. o.zo*/

ZDRNCa0.30

O A T A C R l l 0.1793. 0.1015. 0.1826. 0.1833. 0.1835. 0.?835. 0.1835.

3 0 .1731. 0.1720. 0.1697, 0.1685+ O.16alr 0.1682. 0 .1687. 0.1691. 4 0.1701. O . l713 /

2 a.1830. 0 . 1 0 1 7 ~ 0.1812. a.1802. 0.1163. o. i t t i . 0 . 1 ~ 5 9 . 0.1748.

ZORNC=0.35

DATA GR8/ O * 1 4 M e 0.1465. 0.1495. O.lSO1. 3.1502e Q l 5 0 l e 0.1503.

3’ 0-1411. 0.1403. 0.1386. 0,1378. 0*13;8e 0.1383. 0.1390. 0.13%. 2 0.1415. 00:4a3r 0.1459. 0.1470. 0.1454. 0.1444. 0.1434. 0.1425.

4 o.i4as. 0.1423/

ZORNG-0.40

OATA C R 9 1 0.1173. 0.1192. 0.1201. 0.1205. O o I Z o S . O . l Z C 3 . 0.1202. 2 0.1197. 0.1132. 0.116Z. 0.1175e 0.1162. 9.11’369 0.1146. O * l l 5 8 e

4 0.1152. 0.1168/ 3 0.1120. o. i izz . o . i t i i . 0.1107. 0 . i ~ ~ . o,iizo. 0.~130. 0.1131.

ZDRNG-0.45

OATA GR10/0.0919. 0.0937. 0.0944. 0.0946. 0.0943. 0.0941. 0.0939.

3 O o O 8 1 9 * 0.09*6. 0.0819. 0 . 0 8 6 9 ~ 0 . 0 8 7 9 ~ 0.03%. 0.0902r 0.0910. 4 0.0926. 0.09-J

2 0.0934. 0.0329. 010P2Oe 0.0915. O . O Y W * 0.0898. 0.08911 O.O8&6.

ZDRNCmO. 50

O A I A GRLl/O.07021 O - O ’ l t e 0.072Zr 0.0722. 0.0716. 0.0714e 0.0712. 2 0.0107. 0.0702. OeOb94. 0.0690. 0.0681. 0.0671. 0.Ob72e 0.0668. 3 0.0664. 0.06621 O.Ob6O. 0.0664r C4.0677* 0.0490r O.O?OLe 0 . 0 7 1 3 . 4 0.0733r 0.0752/

: \

ZQQ NG-0.55

I '

C C C

C C C

C C C

C C C

C C C '

L 294-,

221

C

C C C A L C U L A T E S R A T I O O F ORGAN DOSE R A T E TO DOSE S A T E 1N A l R FCR PrlOTOVS AT 0 3 E G : C AND 760 MM PRESSURE US:NG O R G 4 3 OOSE-QATE F A C T C R S FOR MONGE'iERCETIC SOU*CES C A T THE BOW S U R F X I G I V E N BY O * B R I E ! 4 AN0 SANNA. H E A L T H P H Y S I C S 30 . 7 6 C ( 1 9 7 6 1 . A N 0 SPECTEA OF SCATTEP.EO Pcr)TCh!S FOR MONOENERGETIC S O U R C E S I N A Y C I N f I N I T E A T M O S P H R I C CLGUO G I V E N 91 I l I L L M A N . H E A L T H P H Y S I C S 2 7 . 571 (19161: C SEE ECKERHAN. KERR. AN0 R A R I M N . H E A L T H P H Y S I C S 39. 1054 ( 1 9 8 0 1 C C C E - PHOTON ENERGY C

F U N C T I O N F A C t K . €1

I( - INCEX FOR P A R T I C U L A R ORGAN: S E E REFERENCE VALUES OF R A T I O S S I V E V BELOM

O I H E N S I O N EORG(l5lr mG1115). O Q C Z ( l 5 I . O R C 3 ( 1 S l . O a G * t 1 5 1 * 2 ORC5lISlr O R C b ( I 5 l . O R C 7 l I S J r 9 R t 8 I 1 5 J . ORG9t15l. O~CiOl1Slr 3 ORC11t 1 5 1 . O R C l Z ( 1 5 l . O R G 1 3 t 1 5 t . O R G l 4 L l S l . ORGI5(15Is O P C 1 6 ( 1 5 l * 4 ORGl7l IS) 0 O R C 1 8 4 15 1. O R C 1 9 1 1 5 l O U G Z O I 151. O P G Z l t 1 5 ) 9 ORG22t 151 * 5 O R G ~ ~ ~ ; S I . O R C I L S . ~ ~ ~ . ORGF(;SI . EaRcLt 1st

C C ENERGIES FOR R E F E R W C E V A L U E S OF R A T I J S OF ORGAN OOSE RATE TO OOSE R A T E I'i A l a C I N WEV

* . 1 c I C . .

. . r .

C D A T A EORCI 0.010. 0.015. 0.020. 0.030. 0.050e

, i ' 0 . LOO. 0.200. 0.50C. l . O * 1.5. 2.0. 3 4.0. 6.0. e. o* 10.0/

C C R E F E P E N C E VALUES OF R A T I O S OF ORGAN OOSE RATE TO OOSE R A T E I N A I R C C C

C C

. c

C C C

C C C

C C C

0.252. 0.61 5r

0.30 7. 0.63 5.

0.251. 0.710.

0. 7b8. 0.190.

0.22 39

000223

220

ZOVR-R/RANGE C C CALCULATE GEOMETRICAL R E W C T ION PACTOR FOR G I V E N ENERGY AN0 SCALE3 THICKNESS C I N T I S S U E WITc(0UT LEAKAGE CJRRECt l (T4 C

C C CALCULATE LEAKAGE C O R P K T I O N T O GEOWETRICAL REOUCT I O N FACTOR C C CALCULATE PARAMETERS 01 AN0 A C

C=OINTERlEBe ZOVRe ECRe ZORNG. C R e 25. 21. 4 e 25)

Q I ~ Y I N T E R t E B e K R e O1Re 01 30 171 AL-* INTER( €Be ELRI ALRe Oe 3 9 1 7 )

C C CALCULATE SCALED DISTANCE Z / A AN0 PARAMETER 02 C

zOZL=a/IAL.RHO?K I W ~ Y I N T E R C Z C A L . ZOALR. 02R1 0 e 3 r 15)

C C LEAKAGE C C R R E C T I W C

C C CALCULATE GEOMETRICAL R E W C T I O h FACTOR Y1 TH LEAKAGE C l R R E C T I O N C

QL 1.0-0 1.02

G-QL*G I F (G .LT. 0.01 C a O e O RE TURN E NO

,

0002 2 4

i

6294

221

C

C C C A L C U L A T E S R A T I O O F ORGAN DOSE R A T E TO 00% R A T E I N A I R FCR W O T O Y S AT 0 9 E C : C AND 760 MM PRESSURE US:NC ORG4.I OOSE-RATE F A C T C R S FOR MONCE'4ERGETIC. S O U ~ C E S C A T THE BOW SURFACS G I V E N BY O ' B R I E N AN0 SANNA. H E A L T H P H Y S I C S 3 0 . 7 6 C (19761. A N 0 SPECTRA OF SCATTEP.EO P W 7 C Y ; FOR MONOENERGETIC S O U K E S I N 4 Y

F U N C T I O N F A C t K e E )

C l r s F l N ( f E A T M O S P H R I C C L C U O G I V E N 9 Y I l l L L M A N s H E A L T H P H Y S I C S 27. 5 7 1 ( 1 9 1 4 1 : C S E E ECKERWANe KERRe A N 0 RARIOON. H E A L T H P H Y S I C S 3 9 s 1054 ( 1 9 8 0 1 C C K - f N C E X F O R P A R T I C U L A R ORGAN: S E E REFERENCE V A L U E S OF R A T l O S Z I V E Y BELOW C E - PHOTON ENERGY C

D I M E N S I O N EORGIlSIr m G l ( 1 5 1 s O s G Z ( L 5 ) r O R C 3 ( 1 5 1 e O a G b ( 1 5 l e 2 ORC51151r ORC6¶151. ORG7tlSle O R C 8 l I 5 I e O R C 9 ( 1 5 1 . OQCiOlISls

'3 O R G 1 1 1 1 5 ) . O R C I Z ( I 5 l e O R C 1 3 ( I S t r O R G l C L l 5 I e O R G 1 5 l 1 5 l s OPG16115l. 4 ORG17(15Ie C R G l 8 t l 5 1 e O R G 1 9 t 1 5 l e ORCZO(15l. O P G Z I ( 1 5 1 r O R G 2 2 1 1 5 ~ s 5 ORCZ3l15l. O R G I l 5 e 2 3 1 . O R G F f l S l . EORGL(1SI

C C E N E R G I E S FOR REFERmCE V A L U E S OF R A T I O S OF ORGAN OOSE RATE TO OOSE R A T E 1% A I \ C I N MEV C

OATA EORC/ 0.010. 0.015r 0.020s 0.030. 0.050. L 0.100. 0. ZOO. 0.5oc. 1.0. 1.5. 2.01 3 4.0. 6.0. 0. 0. 10. or

C C R E F E P E K E VALUES O F R A T I O S O F ORCPH OOSE R A T E TO OOSE R A T E I N A I R ' c C C

C - c

C

C C C

C C C

C C C

0.30 7s 0.63 5 s

0.251. 0.71 0.

0.22 3.

000225 - . . - .

222

C C C

C C C

C C C

C C C

C C C

C C C

C c C

C C C

C C C

C C C

2 0 . 4 5 4 1 0 .483r 3 0.651 r 0.667.

SMALL I N T E S T I N E

OATA CRC6/ ' 1. ?8E-Oh. 2 0.392. 0.431. 3 0.621 s 00639r

UPPER LARGE I N T E S T I N E

DATA QRG?/ 2. 62E-06. 2 0.493. 0.512. 3 0.652. 0.713.

LOWER LARGE LKTESTI t IE

OATA ORG8/ 2 0- 439 * 3 0.649.

K!ONEIS

OATA ORG9/ 2 0.481 * 3 0.722 m

L I V E R

O A T A O?G10/ 2 0.469t 3 0.655 .

LUNG S

OATA ORGll/ 2 0.522. 2 0.677.

UARRQY .

OkT4 O R G L 2 / 2 O w B b 4 r 3 0- 698.

REO UAAROY

0 4 T A ORC13/ 2 0.41 3. 3 0.713

W A R I ES

OATA OP.G14/ 2 0.401. 3 0.574.

PANCREAS

0.507. 0.694.

4.C4E-O 51 0.538. 0. IS 7.

- 0 . 5 5 6 . 0 . 5 5 6 . 0.710/

3 19E -0 2 4. C 2 E -.O 2 0.506. 0. 51 6 * 0.673/

9.03E-03. 7.50:-02. 0 . 5 9 2 . 0.592 t

0.7b6/

8 . 3 ~ ~ 4 ~ . ~.IIE-o~. i.eoE-02. o . ~ ~ E - o z . 0 . 5 3 8 . 0.554* 0.5951 0.592 * 0.6930 0.726. 0.?49/

0. t35 .

0.21 5. 0. cc 1,

0. 2601 0.675.

0.225. 0.62 3r

0.351. O . C ? 9 r

0- 2899 0.639.

0.32 5r 0.671,

0.58 8r 0 . b8 7.

0.155* 0.6791

0- 235. 0.5r9.

6294- . - . 77 --

223

C C C

C C C

C C C

C C C

C C C

C C

.C

C C C

C C C

C

O . l T 0 . 0.556.

0.60 3s 0.699.

0. 70 7. 0.980.

0- 24 5. 0.61 l e

0.260s 0.62 3 s

0. sa 8. 0. ab 5.

0.61 0. 0.68 3.

0.541. 0.798.

0.198. 0.57 9.

1.31. e t 1 e

e 9 1

- -0002.27

. . I I

2 2 4

6 URGI4tllle I O ~ G ~ l s l S l r O r ( G 1 5 ( 1 ) b e (OPC(lel6le ORGi6(1lle 7 tORGllrl7)r ORGl7llllr fOZC(ls16le ORGl8(11le (ORC(ls19le 8 ORC19~lll~ ~OPCtl~ZOle OPC20tlIle IORC~lrtlI. ORGZl(1lle 9 (ORC(I.22)e ORG22111le (ORG~le231e ORG23(lIl

C

C C CALCULATE R A T I O OF O R G C N DOSE RATE TO DOSE R A T E IN A 1 9 U S I N G L I H E A O C I N T E R P O L A T I O N F O R E N E R G I E S LESS THAN 10 K E Y C

I F ( E .GI. EORGIIII CO TO 2

F A C ~ ~ E / E O R G i l B ~ * O R C i I e l o . GO TO 3

C C CALCULATE LOGARITHHS OF REFERENCE ENERGIES AND R E F F E N C E R A T I O S F3R P A R T I C U L A I C ORGAN C

2 DO I l-lelS EORtLlI ~ - A l O t l E O R G ~ I )l O R G F ( I l ~ A L M ; ( O R G l l r K l l

1 C O N T I N U E t C CALCULATE R A T I O U S I N G C U B I C INTERPOLATI0) ( OF L O G A R I T H ~ S C

F A C a E X P ( Y INTER(AL0CfEIe EORCLe ORGF. 0. 4s 151 1 3 R E T U I N

E NO

\

. 6294 -\ - 225

- C

C C C A L C U L A T E S E X P D ( E N T 1 A L I N T E G R A L S U S I N G P O L Y N O M I A L A N 0 R A T I O N A L A P P P O X I M A l I O l r S : C SEE €OS. 5.1.53 AND 5.1.56 I N H A N 0 6 0 0 K OF H A T H E M A T l C A L F U N C T I O N S e PG. 2 3 1 I:

F U N C T I O N E l t F M e X I

D O U B L E P R E C I S I m A Q C e ALOe A L l e AL2. AL3. A L 4 e A L S

D O U B L E P R E C l S I m O M M e DNOC. FMo X e E l D A T A ALOe A L l e A L Z . A L 3 e Al.41 A L S / -0~5772156600e 0 . 9 9 9 9 9 1 9 3 0 0 .

2 - 0 . 2 C 9 9 1 0 5 5 0 0 e 0 . 05 519968D01 - 0 ~ 0 0 9 1 ~ 0 0 4 0 0 e 0.001 0?85?00/ D A T A bG1. AGZe AC3. AC4/ 8 . 5 7 3 3 2 8 1 4 0 1 D O ~ 18.05901b9~300Oe

2 8.634 76089250D. 0.267773734300f

D O U B L E PRECISJ(IY A C 1 e A C Z e A C 3 1 AGC, B l e 820 83. 8 4

D A T A 81. 821 831 84/ 9.573322345400~ 2 5 . 6 3 2 9 5 6 1 4 8 b D O e

A R C - F W X 1F (ARC . C l . 1.0001 GO TO 1 El-AL0*AL1*ARC*AL2.(ARC..2.1*AL3.(ARC~3. 1oAL4*(ARCa*4.J * A L 5 *

i 2i.099t,s30et700e 3,958+969tteoo/

2 t ARG**5. J -DLOGl ARC) 2 RETURN 1 ONUW=ARV*4. AG1* t A R V * 3. t .tiCC.( ARC.* 2. *AG3*ARG *A (;c

DNCM-ARW.4. *81*( A R C . . 3.8 * W * t ARV.2. ) + 8 3 * A R G * B 4 El-DNU(r/lDWOT*ARCoCEXP(ARCl t

E N O t a TO 2

226

C SUBROUTINE B S P K (EN. F I t EBSRe ATNO- N C D t F I E . JSPEC. E M I D I -

C C C C C C C C C C C C C C C C

C

L C CALCULATES W M B E R OF ELECTRONS A S A F U N C T I O N OF ENERGY FOR C O l T l N U O U f -SPECTRA

FROM BETA OECAY: SEE EQS. 13.1Z)-(3.141 A N D ' ( 3 o Z Z I OF EVANS. THE ATOMIC NUCLEUS

E N - ENDPOINT EN€RGY FOR C O N T I N U O J S SPECTRUM F I - TOTAL I N T E N S I T Y COR CONTINUOUS SPECTRUM EBSR - ARRAY OF E N E R G I E S FOR C A L C U L A T I O N OF CONTINUOUS SPECTRUM ATNO - AYOMIC W M B E R OF PARENT R A D I O N U C L I D E NCD - I N D E X FOR m P E O F ELECTRON

F I E - ARRAY CF ELECTRON I N T E N S I T I E S AT E N E R G I E S G I V E N B Y ALTERNATE VALUES OS

JSPEC - INDEX S P E C I F Y I N G WIGWEST FULL ENERGY I N T E R V L L CENTERED at AN ALTERNATE VALUE OF EBSR FOR Y H I C M I N T E N S I T Y IS ION-ZEPO

E N I D - ENERGY S P E C I F Y I N G L A S T ENERGY I N T E R V A L I N SPECTRUM I N C L W I N G ENDPOINT

EBSR

D I M E N S I O N E B S R I l l r F 1 E l l ) t ~ I B S I l t 0 l ~ t ELOY13)r F L O w ( 3 D t CCWPLEX-16 Z l r DCGdWt GAM

C E L K T R O N REST MAZS I N MEV C F I NE-STRUCTW E CONSTANT C

C C D E F I N E FUNCTIONS FOR CONTINUOUS ELECTRON SPECTRUM C C S T A T I S T I C A L FACTCR FOR ALLOYED SPECTRUM C

C C , F I k S T - F O P I I D D E N W I O U E C O R R E C I O N FACTOR C

C C COULOMB CORRECTION FACTOR C

C C I N l T l A L I Z E S T A T I S T I C I L FACTORS AND NU'IBER OF ELECTRONS AS A FUNCTIPI O F EYEP.GY C

DATA Em. Fsc/ o.si09x.. T . Z ~ T ~ E - O ~ I

FOtY. ETA. VO)~NoETA-(lWO-U).*2.)

F 1 i W . E T A S W O I ~ E T A ~ Z . * ( W O - Y I - * 2 .

F C l E f A , r S r It ~ N S O I ~ i E T A ~ ~ l 2 ~ ~ S ~ I ~ E X P l 3 . l 4 ~ S 9 ~ Y t * G A H S O

DO 10 I ~ l t l 2 0 1 FIBSf II-0.0 I F I 1 .CT. 600) GO T O IO F I E l I ! r O . O

10 C O N T I N U E C C CALCULATE ATOMIC NUMBER OF DAL'GMTER N U C L I D E c

IF 1 I A B S l N C D ) -EO. 11 ZD-ATNO* l . I F I I A B S I N C D I .EO. 2 ) Z D = - I A T N O * l . I

C

000230

227

*- .?a .. ... .

C CALCULATE S T A T I S T I C A L FACTSR FOP ELECTRUN SPECTRUM A T ENERGIES G I V E N BY VdLUES OF EBSR: C A L C U L ~ T E I N T E G R A L OVER ENERGY OF S T A T I S T I C A L FACTORS U S I N G C

C C C C C

C C C

C C C

C C C

C C C

C C C

C C C

C C C

C - c

C

C C C

C C C

T R A P E Z O I D A L RULE

l N l T l A L l L E I N T E G R A L PND SET FXPST-FORBIDDEN LHIOUE COPPECTIDN FACTOD FOP 4N ALLOWED T R A N S I T I O N

AREA-0.0 FlC-1.0

CALCULATE ENDPOIN? EriERGY IN UPl lTS OF ELECTRON REST MASS

Y O 4 N / E W ) * l .

CALCULATE C D N S T A M TERM IN COULOWB C O R R E C T l O N FACTOR

5- SORT I J - I A 9 S t LO I *F SC l**2. I -1

C A L C U L I T E S T A T I S T I C A L FACTORS AS A F U N C T I O N OF ENERGY

00 1 I-Z*ltOl I F (EBSRIII .CTo EM1 GO TO 2

CALCULATE ELECTRON TOTAL ENERGY A N 0 WWENTUH

W E B S R ( I I / EM 1 E 1 A= S CZT t Y*Y- 1. I

CALCULATE F I R S T - F O R D I O D E I W I O U E CORP.ECTION FPCTOR

I F I N C D .LT. 01 F l C - F l l Y e ETAS YO1

CALCULATE TERRS I N C W L G H B CORRECTION FACTOR

r - z C ~ ~ f C ~ w / E T 4 Zl-OCRPLXl EDLE( 1. *SO s CAf4-DCG34I 21 I CAMSQ=CAU~DCCNJGl GAM)

CdLCULATE S T A T I S T l C A L F A C T W

O B L E t Y I I

F lus ( I I = F O ( W . . R A I W O I * F l C * F C I E f A r 5 e Y s GAM508 COST I KUE

SET INDEX F O R LAST E h i R Y ZN SNERGY AND S T A T I S T I C A L FACTOR ARRAYS

NSPEC-1-1

CALCULATE S T A l l S T l C 2 L FACTOR AT L E P O ENERGY USING O U A D R I T I C E X T R A P O L A T I O N

DO 3 I - 1 . 3 E L O M ( l ) - E e S R l r ~ l t F L O Y t I 8-F I €5 I I *I I CONTINUE F I B S I 1 l=r l N T E R 1 E B S E I l l ~ E L m e FLOW, 01 3 s 31

CALCULATE I N T E G R A L O F S T A T I S T I C A L FACTORS

00 4 fmZ*NSPEC

228

4 C C C

C

A R E A ~ A R E A * O . 5 * I F I B S I I I , F I B S l 1-11 I * l E B S R l II-EBSPI 1 - 1 ) ) CONT I NUE

A00 COFiTRlBUTIDN FROM ENERGY I N T E R V A L C O N T A I N I N G ENOPOINT ENERGY

AREA-LREA*O.S*FIBS I N S P E C ) * [ EN-EBSR I N S P E C I I

C CALCULATE NUMBER of ELECTRONS PER OISINTECRATION A T ENERGIES :IVEY EI C C C C

C C C

C C C C

~. - - ALTERNATE VALUES OF EBSR US!% SIMPSON'S R U L E

CALCULATE I N T E R V A L Y101H A N 0 S P E C I F Y INDEX FOR ENESGY FOR L A S T F U L I N T E R V A L

OELEN=EBSR 12)- E B S R l l I JSPEC-NSPEC-b ,

CALCULATE S P E C t U V l l

OD 5 I - 2 - J S P E C . 2

J - 1 1 2 F I E ( J ~ - F I * O A R E W A R E A

O A R E A = J E L E W ( F I B S I I - l J * F I B S l I * l J * 4 . * F l B S ( I J J / 3 0

5 CONTINUE

CALCULATE C O 3 T R I G U T l O N TO SPECTRUM FROM ENERGY I N T E R V A L C O N T A I N I K ; FYDPCIIYT ENERGY ey BISECTING INTERVAL AND USING SIMPSON'S RULE

6

7

I F I 1 .EO. J S P K J GO TO 6 EMID=l EBSR( J S P EC I * E N ) / 20 F B M I D ~ Y I N T E R I E W I O I EBSRe FXBSI 01 31 NSPECt DbREA- 1 EN-EM10 ) * ( F I B S ( J S P E C t + I o * F B M f O 1 / 3 0

c-L' TO 7 -

k b h r D = Y I N T E P f E M ! O . EBSRI FIBS* 01 31 N S P E C t OAR E A- I EN- EM I 0 I 0 I F I B S t N SP E C t *4. i B M I O I / 3

f ; 3 = l E B S R ( N S P E C l *ENl/Z.

F I E t J * l I = F I * O A R E A / A R E A RETURN E N 0

6294 . _

229

C

C C CALCULATES I N T E G R A L OVER CONTAMINATED GPOUJO S W F A C E OF ELECTRW: SCALFO P’JI‘4T C KERNEL t N A I R C C EB - ELECTRON ENERGY FOR EVALUATION OF INTEGRl lL C RNCAR - REFERCNCE ARRAY OF ELECTRON RANGES I N A I R IN G / l S O CMI r T EYEBGIES C G I V E N BY V A L U E S OF EBR BELOW C R - OISTANCE ABOVE GROUNO Fm EVPLUATION OF INTEGRAL I N C / l S Q ‘:MI C RANGE - ELECTRON RANG€ I N A I R I N G / l S O C W I FOR ENERGY € 0 C L I N T - INTEGRAL OVER CPOUNO W P F A C E OF ELECTRON SCALEO OOINT K 1 * M L I N A19 C FOR ENERGY E B bW0 OISTANCE ABOVE GROUNO R C

SUBPOUTtNE OGRNO IEB. RNGTRI Re RANGE. € I N T I

O IMENSION R N C A R ( I ? * E A R t 8 I m A L P H A R l B l r E A R L t 8 I 01MENSION REOISR(251. E B R l 2 5 l r S P K R l t 2 5 I r S P ( ( R 2 t 2 S l s S P K R 3 1 2 5 1 r

2 S P K R 4 t 2 5 I S P K R 5 1 2 5 I o S P K R b ( 2 5 1 SPKRTI 251. S P K R B t Z S I S P I R 9 l Z 5 I I 3 S P K R l O [ Z 5 1 S P K R l l t 258 S P K R l Z t 251 S P K R l 3 1 2 5 I w SPUR 14125 I. 4 S P K R 1 5 f 2 S I 9 S P I R 166 251 e S P K R l T ( 2 5 I S P K R I O I 2 5 1 SPKR 191 25 I* 5 SPKR2OfZSI . S P K R Z 1 3 2 5 l . S P K 9 2 2 1 2 5 t r SP ILR2312 f l . S P K R 2 4 t 2 5 l r 6 S P K R 2 5 1 2 5 l . SPKR(25.251

2 O I S L R f S I O I M E N S I a ( A L W E R l 2 5 l r F A I R R t 251251. R I N f Z E t 2 5 . 2 8 1 1 D l S P t 2 8 I . .

C C RATIOS OF OfSTANCf CROW SOURCE P O I N T TO ELECTRON RANGE FOR R E F W E W E VALUES Os C ELECTRON SCALEO P O l N T KERNELS C

OATA R E O I S R I 0.01 0105. 0.101 0 . l S r 0.20e O o Z S r 0.301 0 .35 . 0 . 4 0 . 2 0.45r 0.50. 0.55r 0.60. 0.65r 0.70. 0.751 O.8Or 0.85. 0.901 O.95r 3 1.03. 1.05s 1.10. l . l S r 1.201

C C RATIOS C f O t S l A N C E FROM S W R C E P O t N T TO ELECTRON RANGE BETWEEY 0.0 AN0 0.0s AT C WHICH REFEREkCE ARRPV OF INTEGRCLS I S TO OE CALCULATED C

C C ENERGIES FOR REFERENCE VALUES S ELECTROW RANGES A N 0 SCALEO P O I N T KERNELS C

DATA -0lSLRI 0.001. 0.0021 O.OO5r 0.011 0.021

OATA €OR/ 0.010. 0.015. 0.020. 0 . 0 3 . 0.040. 0.053. 2 0.0bOe 0.0801 0.100. O . 1 5 0 r 0.200. 0.300r O.*W* 3 0.50Oe 0.600. 0.eC01 1.OI 1.5. 2.00 3 . 0 . 4 4-01 5. 00 6.0. 0.0. 10.01

C C REFERENCE VALUES OF ELECTRON SCALED P O I N T KERNELS t N WATER C c REoISn=O.O C

OATA S P K R l / 0.508r 0 .508 . 0.510. 0.521. 0.928. 0 . 5 3 6 . 2 0.544. 0.559. 0.5t21 0 .595 . O . 6 l l r 0.640. OobbO* 3 O.674r 0.b89. 0.714. 0.73br O . 7 l l r 0.798. 0.821. 4 0 . 1 ~ 5 . 0 . 8 4 ~ . o.e*i. 0.1339. o . 8 ~

C C R E O t Sa=0.05 C

DATA SPKR2/ 0.588. 0.582r 0.576. 0.579. O-SBZo O.58br

000233 \

4 . . /"

.. . .

230

2 0.592 e

3 0.708. 4 O.8t8.

C C REO1 SU=0.10

0.603. 0.612. 0.727. 0 * 7 5 2 e 0.875. 0 . 8 7 1 .

0 . 6 3 3 . 0.648. 0.674. 0. 7 1 4 s 0.811. 0.834. 0 . 8 7 3 . 0 .867/

0 .b90e 0.856.

C OAT& SPUR)/

2 0.6401 3 0.144. 4 0.900.

C C RED1 SR=C. 15

0.663. 0.654. 0.645. 0.b48r 0.157. 0 .784 . 0.905. 0,906e

0.648r 0 . 6 4 3 . 0.640. 0.661. 0.67er 0.702.

0.903. 0,897.' o.-eot, 0.845. o . a b .

C OATA S?KR4/

2 0.688. 3 0.184. 4 0.924s

REDISR=O.ZO

DATA SPUR51 2 0.740s 3 0.821. 4 0.950r

R ED! SR-0. 25

D A T A SPUR61 2 0.810.

. 3 0.865. 4 0.910.

RED 131-i.22

D A T A s?r.Fi/ 2 0.9db e

3 0.919. 4 0 .97be

0.733r 0.717. 0.691. 0 . 6 Y 2 e 0.795e' 0.8201 0.929. 0.930r

C C C

0 .803 . 0.781. 0.741. 0.744. 0.8329 0.860. 0.949. 0.948.

0.769. 0.754. 0.746.

0 . 8 6 7 s 0,891. 0.920. 0.941 e 0.936/

0.157. o.7ro. 0.791. 0.140. 0.801. 0.941 e

c C C

0.994. 0.8690 0.809. 0.8081 0.876s 0.692 e 0.961. 0 . 9 U r

0.855. 0.831e 0.820. 0.8201 0 .828 . 0-945. 0.905. 0.935. 0.952. 0.951. 0.946/

0 . 8 1 4 . 0.855. 0.967.

C C C

0.990s 00961s 0.901. 0.894. 0.924. 0.936. 0.9tb. 0.972.

0.954r 0.932. 0.920. 0.89B* 0.9G3e 0.998. 0.949. 0.969. 0.960. 0.963. 0.9561

0.912 e

0.912. O.979r

C C C

REDISR=0.35

D A T A S P K R B l 2 1.009. 3 0.995. 4 1.002.

REDISR=0.40

DATA S?KU3/ 2 1.134. 3 1.104. 4 1.028.

RESISR=O.&S

D A T A SvKP.lO/ 2 1.292. 3 1.247. 4 1.066.

1.084. 1.0621 1.005. 1.003. 1.010. 1.012. 0. 996. 0.992 e

1.050. 1.032. L e O Z Z e 0.998. 0.997. 0.996. 1.003. 1o007. 1.010. 0.9801 0.9641

1.C10. 0.9% 1.007s

C C C

1.195. 1.1721 1.131. 1.131r 1.099. 1.088. 1.010. 1.300.

IrlsO. 1.109. 1.043.

C C C

000234

6294 .

'.

231

C C C

C C C

C C E

C C C

C C C

C C C

C C

' C

C C C

C C C

REOISR=0.50

D A T A SPKRl I/ 2 1.42 8. 3 1 . 3 8 4 . 4 1.119.

REDISR=0.55

DATA S P K R I U 2 10556. 3 1.498. 4 10193.

REO1 a R - 0 . 6 0

DATA SPKR13/ 2 1.62B. 3 1.579. 4 1.259.

REOISR-0.65

DATA SPKR14/ 2 1.634. 3 1.605. 4 1.303.

RED! SR-0.70

DATA SPURIS/ 2 I ,528. 3 1.522. c 1.313e

UED!SR-0.75

DATA SPKRLSI 2 1.336. 3 10351e 4 1.265r

REO!SR-O.80

i DATA SPURIT / 2 loO76r 3 3.070. 4 1.125e

REDISR-0.85

DATA S P K I l B / 2 0.764. 3 0.736. 4 0.900.

REDXSR-0.90

1.391 v 1.432. 1.355. 1.0651

1.415. 1.561 e 1.457. 1.119.

1.519. 1.645. 1.529. 1.113.

1.503. 1.649r 1.555. 1.217.

1 .*25 . 1.557. lr4e9r 1.242.

1.274.

1.389. 10 426

1.032. 1.31s.

1.479. 1.551* 1.435r 1.066.

1.540e 1.643. 1. 501 1.110.

1.528. 1.653. 1.529r 1.147.

1.449. I. 563. 1.475. 1; 179.

10239.

1.074. 1.073. I.Ob+. 1.!31.

o.ei9. 0.752r 0-7421 0.962.

1.603. 1.428. 1.28s. 1.0041

1.503. 1.536. 1.380. 1.024/

1.578. 1.639. 1.438. 1.0541

- 1.582. 1.651. 1.472. 1.08aI

1.47Pe

1.4$3* l.t24/

1.5588

1.315. 1.359. 1.3191 1 .1361

1.090. 1.072. 1.017. 1.1nz/

0.7%.

00 165 0.998 /

0.14a.

1.417. 1.405. 1.232.

1.525. 1.5221 1.325.

1.607. 1.622. 1.393.

lmb09. 1.635e 1.423.

1.501. 1.544. 1.413.

1.323. 1.361r 1.3130

1.084. 1.071 1.088*

0. TCO. 0.735. 0. at.

1 i

1.624. 1 .395r 1.161.

1.550. 1.5071 1 . 2 4 ~ .

1.622. 1.604. 1.318.

1.624. 1.622. 1.360.

1.516r 1.5%. 1.358.

1.328. 1.359. 1.2#1.

I .CEO. 1.071 e 1.1 11.

0.761. 00735. 0.842.

I .

C C C

C C C

C C C

C C C

C C . C

C C C

DATA S P K R 1 9 / 2 0.484. 3 0.422. 4 0.609.

RED,!SR=0.95

DATA SPKRZO/ 2 0.284. 3 0.185. 4 0.311.

R E D I S R - 1 . 0 0

D A T A SPKR21/ 2 0.12br 3 0.058. 5 0.129.

RED!SR-l.O5

DATA IPUU22/ 2 0.061. 3 0.010. 4 0.028.

R E D I S R - 1 . 1 0

D A T A S P U R 2 9 2 0.013. 3 0.002. 4 0.005.

RED!SR-1*15

DATA SPUR24/ 2 0 . O O C . 3 0.000. 4 0.001.

R E D l S R - 1 . 2 0

OAT) 2 3 4

C D A T A

2 C

0 . s h e . 0.469. 0.424. O.bS4r

0.329. 0.248. 0.183. 0.352.

0. 179. 0.114. 0.051. 0.155.

0.070. 0.058. 0.010. 0.036.

0.024. 0.011. 0.002. 0.038r

0.000. 0.000. 0. 090. 0.002.

SPKRZSI 0.000. 0.000. o*ooo. 0.030. 0.000. 0.000. 0.000.

0.558. 0.661 e 0.427, 0.694.

0.339. 0 . 2 3 7 . 0.104. 0 . 3 8 8 1

0.185. 0.100. OwOSbr 0.181.

0.072. 0.042. 0.009. 0.045.

0 . 0 2 3 . 0.009. 0.001 . 0.012.

0.000. o.oG0. 0.000. 0.003.

C.OOO. 0.000. 0 .000. 0.000.

232

0.5S2e 0044b. 0.431 01 756.

0.335. 0.219. 0.191 0.465

0 . 1 9 1 . 0. oe6 . 51058. 0.235 *

0.013. 0.026 * 0.008. 01067e

0.021. 0.001. 0.001 . 0.018.

0.000. 0.000. 0.000. 0.0c6.

0.090. 0.000. 0.000. 0.001 .

0 .523 . 0.438. O A 5 S e

0.803/

0.313. 0.213. 0.206. 0 .542/

0.104. 0.07b. O.OCba 0.295/

0.074. 0.020. 0.008. o.o?a/

0.019. 0.005. 0.001 O i O 2 5 /

0.000. 0.000 0.000. 0.008/

0.3CO. 0.000. O.COO. 0.003/

0.5061 0.429. 0.40lr

0.290. 0.193. O*230*

0.148. 0. Gbbr 0 . 0 7 8 1

0.0721 0.014s 01013.

0.01be 0.003s 0.002.

01000. 0. 000. 0.000.

0.000. 0. 000. o.ooo*

0 . 4 9 2 0.625. 0.5 52.

0 . 2 7 C e 0.189. 0.273.

0.136. 0.013. 0.10~.

0.010. 0.012. 0.020.

0 . 0 1 5 . 0.002. 0.003.

0.5009 0.000. 0.001 e

0.u00. 0.000. 0.000.

FOP RIFEPENCE VALUES OF S C A L I N G PARAMETER

EAR/ 0.010. 0.020. 0.050s 0.100~ 0.200. 0.500. 1.0. 2 . w

C REFEPENCE VALUES OF S C A L I N G PbRAMETEP TO CONVERT ELECTPDN SCALED DO!NT KCSYELS

C c IN W A T E R TO VALUES IN AIR

DATA ALPMAR/ 1.025. 1.023s 1.0221 1.021. 1.021. 1.022. 1.0201 ' 2- 1.014/ '-

C C OEF!NE E O U I V A L E N T T w 0 - 3 1 M E N S I C N A L APRAT OF ELECIPDN S C a L E D PO!NT KEoNE1.S I N

000236

233

... --.

YAT EP

C TEST FOR FIP.ST T I M E THROUGH SUBROUTINE C

IF (.NOT. F I R S T I GO TO 1

C C C C C C C C

C C C

C C C C

C C C

C C C

C C CALCULATE T M - D I M E N S I O N A L REFERENCE ARRAY OF INTEGUALS OVER GUOURO SURFACE 9F

ELECTPON SCALED P O I N T KERNEL I P J A IR AT ENERGIES G I V E M BY VALUES OF EBR APJD

C

AT LOWER LIWITS OF INTEGRATION GIVEN er VCLUES OF R E D ~ S R GREATER THIN 0.0 PLUS SELECTED VALUES BETWEEN 0.0 hND 0.05

CALCULATE ELEtTRO)J S C L L I Y G PAPAMETERS TO CONVERT SCCLEO P O I N T KEPNELS 1Y MATER fo VALUES I N A I i t AT ENERGIES G I V E N BY EBR USING LOGARITHMS OF ENERGIES EAR FOR I H I E R P O L A T I U 4

DO 2 I - l r 8 E A R L l I l - A L C S I E A R t 1 t B

DO 3 1-1.25 A L P H i R l 1 ) ~ Y l N T E K l A L O ~ I E ~ R I I ) l e EARL, ALPHARe 01 3s 81

2 CONTINUE

3 CON1 1 HUE

CALCULATE TMC--3InENSIONAL ARRAY OF SCALE0 P O I N T K:ERNELS I N A I R

00 4 111.25 00 5 J m l r 2 5 I F (J .LE- 2 3 ) GO TO 10 - SCALED PGIh7 KERNELS I N A I R ARE TAKEN E O U A l TO VALL'ES I N W A T P AT TU0

LARGEST DISTANCES

F A I R R l I e J l ~ S P K R l I ~ J J GO TO 5

CALCULATE SCALED DISTANCE I N A I R

10 ATR-ALPnER I I l * R E D I S R l J l

CALCULATE SCALE0 P O l W KERNEL IN A I U

S A I R R I 1 J l +ALPHER1 I J * ? I N T E R l E B R I 11 ATR e Em* REO1 9 SPKR. 25. 2 24s 4. 251

5 Cl)NTINUE 4 CONTINUE

.- . .

234

C C

C C C

C C C

C C C

C C C

C C C C C

C C C

C C C C

CALCULATE INTEGRA1 5 AT EACH ENERGY USING SIUPSON'S RULE

00 6 1-le25

CALCULATE INTECRALS AT REDISR=O.OS* 0.15. 0.25s 1-15

00 7 J-2~24 .2

1 N I T l A L I Z E I r s l E R TERNS I N SIMPSON'S RULF '

12-0.0 13-0.0

CALCULAYE OUTE?. TERN ASSUMING SCALED POINT KERNEL IS ZERO

T I =FA I R R I I JJ / R E D I SRt J I

CALCULATe INNER TERMS

JI-J* I 00 8 K-Jle25.2 TZ=TZ *FAIRRt I

IF t J .EO. 241 GO TO 11

00 9 K=J2e24e2 13=T3*FAIRR[ I e K l / Q ED I SRtK 1

K I I R E D ISR I K 8 8 CONTINUE

J2=J* t

9 CONTINUE

I

T REOISR-I .2S

REDEFINE INDEX FOR VARSAbLE R E O I S R SO T H I T VALUE I f S I X I T RED1SR~O.OSZ T H I S ALLOHS ROOM FOR CALCULATING INfE\-%IALS FOR F I V E VALUES OF REDISP. BETWEEM 0.0 &NO 0.05

11 )(-.I**

CCRBINE T E R M TO OBfaIH INTEGRCL; INTERVAL YIOTM I f 0.05

P?NTZE[ I .K# -Oo OS*tTl*4.Dof2*200*T3 113- 7 CONTINUE

CALCULATE INTE@*LS AT R E D I S R - O - l O e 0.20. 0.309 o o o m 1.10 USING fa *€ PROCEWRE AS ABOVEe EXCEPT FOR ASSURPT,IO?4 FOR O U T E R TEPP

00 12 J=3*23wi 12-0.0 13-0.0 Tl=FAIRRI I * J l 1REOfSRlJ)'FA WRI 1 s 2581REDI S R I 25)

W 13 K ~ J l * 2 4 e 2 12 -1 2.FA I R R t I e I( I /RED ISR ( K I

1 3 CONTIMJE 1F ( J .EO. 231 GO TO 14 J2=J*2 00 IS K-J2.2302 1 3 = 1 3 * F A I R R [ I eKI /REDISR(K9

J l -J * l

15 CONTINUE 14 K=J*4

I t CONTlNUE R 1 NTLE ( I e KJ-0 0 05. 11 *4.0*12* 2.0.13 1 I 3

.

,_ .

- . 6894

C C CALCULATE I N T E W A L S AT REDISP~O.001v O.002e 0 . 0 0 5 ~ 0.01e 0.02 BY ASSU’ I IYC C THAT SCALED POINT KEP.NEL FOP ANY ENERGY V A R I E S L I Y E A R L Y Y I In SCALED C O!STL?JCE FOR VALUES BETYEEN 010 AN0 0.05 C

, O O ( 7 K~l.5

2 R I N T L E ( I I(. )=FA TRR I I e 1 I* ALOGI 0- 05 I D I SL Qf K t I f ( F A I R e ( I .Z 1-

F A I R R I 1 1 t )10.051* IO~OS-CISiRIK 1 I eR !%‘LE( . I e 61 17 CONTINUE 6 c o r n 1 r r t t E

C C D E F I N E NEY R E F E R E N C E ARRbY OF SCAl ED O!SlrYrCES C O R R E S ? O N D I K 10 LObEP. L I M I T S C OF INTEG;F1AlICN FOR Y H I C H REFERENCE INTECAALS YERE CALCULATED: RESET LOGICAL C V M I A B L E C

16

’ 18

C

DO 16 1-115

C O N I I N U E 00 I8 lrle23 DISRIl~5l-REDIfR~!~I1 CONTINI IE

DI SR( I t - 0 1 S L R l I 8

F I R S T = . FALSE.

c CALCCiLAfE ELECTRON RANGE I W A I R FOR ENERGY C

1 R A N G E ~ Y I N l E R ~ E B e EBRm RNGAR. 0. 3v 251 C C CALCULATE INTEGRAL OVER ZRDUNC SURFACE FOR C R C

TLOLCEF;=R/R PNGE

E B IN C I C S O cni

ENERGY EB AND O l S t A N t E A90VE CSOUW

! I'

236

C

C C PERFORMS LAGRANGIAN I N T E R P O L I T I O N OF A FUNCTION OF TWO V A R I A B L E S C C BASE0 ON DOUBLE P R E C I S I O N I N T E R P O L A T I O N F U K T I O H OLAG OE5CRIBEO I N U r l I O N C CAR8 IO€ P U S L I C A T I O N CTC-?9 C C XX - ABC15SA OF O E S I R E O I N T E R P O L A T I O N P O I N T C YY - OROINATE OF O E S I R E O IMTERPOLATION P O I N T C X - S I N G L Y OIMENSIONEO ARRAY OF A B C I S S A S C Y - S I N G L Y OIMENSIONEO ARRAY OF ORDINATES C Z - DOUBLY O I H E N S I O N E O ARRAY OF F U N C T I O N VALUES G I V E N BY Z l I . J B = C C NX - NUMBER OF ELEMENTS FCR THE X-ARPAY C Kf - NUMBER OF ELEMENYS FOR THE I - A R R A Y C M - NUMBER OF P O I N T S IS M*M FOR THE I N T E R P O L A T I O N C IO - FIP.ST D I M E N S I O N OF Z I N C A L L I N G PROGRAU C

F U N C T I O N O I N T E R I I X . YYr XI I. L e NXI M I Mr I O 1

F I X ( I I r Y I J I 1

O I R E N S I O N L l I O I 1 l e X ( 1 I e Y I L I I X t A t 1 1 0 0 l L O G I C A L OUITXI O U I T Y

C C I N I T I A L I Z E C

2U I TX 0 P A L SE OUITY=.FALSE. M I - M I EXTX=O LEXTY-0

E C F I N O THE R A K E OF 1 N T E R P C L A T I C N A L m G X c -

10

20

30

40

so 6 0

7 0

eo

90

I F t H l .LE. N X I GO T O 10

DO 20 I - I INX I f t X X - X t I l l 3 0 . 901 20 C O N T I N U E I EXTX= L GO TO BO M I O % = I I F I M I O X .6T. 11 GO TO 40 I E X lX1-1 GO TO 50

I f X P T o M I D X - l M l / 2 8 GO TO 60 I SXPT=MIDX- l I M L * l l / 2 1 I F I I S X P T .CT. 01 00 T O TO 1 S X F T = l I E X P T - I S X P T * W l - l I F I I E X P T .LE. NX8 GO TO 100 I SXWT=YX-!41*1 IEXPT-NX GO TO 100 O U 11x1 .TRUE.

U l = N X

I F l A B S 1 X X - X l M I O X l I .GE. A B S l X X - X l M 1 O X - l l I l to TO 50

!

237

C C F I N O T H E P.ANCE OF I N T E R P O L A T I 9 N AL(ING Y C

100 M l - H I F 1 M 1 .LE, N Y I GO TO 110 M l = N Y

I F ~ Y Y - Y I J I I . l 3 O e 1901 120 110 DO 120 J - l e N Y

I20 C O N T I N U E I EXTY = I GO TO 160

I F I M l O Y .GT. 1.1 GO TO 140 I E X T Y - - 1

130 M I O Y - J

GO TO 150

X S Y P T ~ W 1 O Y - l M l / Z I GO TO 160

140 IF i A a s ( y y - v i ~ ! o y i i .GE. A e s ( y y - y r n I o y - l i i ~ GO TO 150

I50 I S Y P T - H I O Y - 1 l!41*1a/29 160 I F I I S Y P T .GT. 01 GO TO 110

110 I E Y P T a I S Y P l * M l - l

180 I S Y P T - W - M l * l I E Y P T - H I GO TO ZOO

190 PUITY-.TRUE.

I SYPT- 1

I F ( X E Y P T .LE. N Y t GO TO 200

ZOO I F ( O U I T X .AND. O U f T Y l GO TU 270 XF ( O U I T X .&MOO -NOT. O U X T Y I CO TO 240 I F (.NOT, aur ix ANO. OUITYI GO TO 230

!NTEP.PULATE A L O S X

210 00 220 K m I S Y P T r X E Y P T 220 C A U I N T E R ( X X c I l l . K I a X. ISXPT. I E X P T I X L L G I K I I

230 C A L L I N T E R I X X e L I l e J I v X. I S X P T I I E X P T I X L A G I J 8 1 GO TO 260

O I N T E R - X L A G ( J l GO TO 280

I N T E ~ P O L A T E ALOXG Y

240 00 250 L ~ I S Y P T e I E Y P T 250 X L A C l L l = L ( 1.L) 260 C A L L I N T E R I Y Y e XLAGe Y e I f Y P T e I E Y P T e Y L A C 8

DIWTER-YLAG GO TO 280

270 nlNTER-L( 1-21 280 RETURN

EN0

000241

230

\

C

C C AN I N T E R P O L A T I ~ R W T I N E DESCRIBED I N UNI(II CARBIDE PUBLICATION CTC-39

SUBROUTINE INTER l P 1 1 FUN. OR& 1SPT. I E P T . N A G )

C

10 20 30

DIMENSION F U N t l ) . O R D t l l r*3-0.0 PROD-I. 00 30 J * I S P T * I E P T PROD-P~DD. tPT-ORDt J l I DENOM-1. DO 20 K - I S P T * I E P T I F t K .NE. J I GO TO 10 0 - P T GO TO 20 P O R D t J I OE W-DEHOC1.t D-ORD t K 1 I SU#-SUM*FUNtJ IfDENOM ALAG-SU#.PR(n RETURN END

i

000242

6294

- _

239

C

C C CALCULATES GAMMA FUNCTIONS OF A COWLEX ARGUM5hT USING A S P I E S EXPANSION: SEE C EO. 6.1034 Ih' HANDBDOK OF MATHEWATICAL FUNCTlONSr PGo 256 C

FUNCTION OCCAM ( 2 )

COMPLEX*16 2. SUM. DCGAN DOUOLE PRECIS I M C (268 DATA c/ 1.0. ~ . ~ I z I ~ ~ ~ ~ ~ o ~ s ~ z ~ D - o I . - ~ . 5 5 ~ 7 e 0 ~ 1 5 2 0 2 5 3 ~ 0 - o i .

! - -- z

240

C

C c SORTS A ONE-DIMENSIONAL MRAY IN DECREASING NUMERlCAL OROER C c N - NUMBER OF ELEMENTS I N ARRAY c A - INPUT ARRAY c 8 - SORTED ARRAY C

SUBROUTINE S O R T (Ne Ar 8 )

OlMENSION A t l l r 8t11 Nl-N-I DO 1 I S l . N l N1-N-I DO 1 K- lrNI I F ( A I K I .LE. AlK611t GO TO 1 T-AtKJ A(K#-AtK*11 A I K*L) -T

1 CONTINUE DO 2 1-1.N w1 -+I 1 I ( I ) - A ( N I I

2 CONTINUE EETUIN END

.

0 0 0 2 4 4

241

C

C C WRITES DOSE-RATE FACTORS I N TABLES AN3 ON PUNCHEO CAUOS

SUBROUTINE O O S W T

C DIMENSION INUCLCZ). T H A L F O I DIMENSION CCSORGI3.231. 0 0 S O R B I 3 r 4 l o OOSSKNI31 e O O S E F F t 3 I CONMON/ B L K I / INUCL. THALL COMUON/ BLKS/ COSORt. DOSORBe OOSSKNI OOSEFF

C C NAXIMUW NUNBER OF L I N E S OF Ol f lWT PER PAGE FOP. EdCH T I P E . O F W S E - @ A l E FACTOR C TABLE C

C C NUMBER W L I N E S OF W T W T BETWEEN SPACES FOR SUMMARY TABLE OF ODGAW AN0 C EFFECTIVE DOSE-RATE FACTORS C

C

C C TEST FOR F I R S T T I M E TnilOUGH SUBRGUTINE

‘ C

C C l N I T f A L I Z E L I N E C G W T S U I T H I N EACH TABLE AH0 RESET L O t l C A L VAEIABLE C

DATA MAXLOF/CO/* UAXSKN/SO/* )IbXSKT/SO/. NAXEFF/SO/

DATE MMSY.P/S/

LOGICAL F I R S T / -TRUEo/

I F CoHar- F I R S T 1 GO TO 1

L I NORC=O L I NSKP-0 J

L I NSKS-0 L I N S R T - 0 L I IdEFF-0

I

FIRST-.FALSE. C C WRITE 00SE-RATE FACTORS I N TABLES C C PHOTON DOSE-RATE F I C T O R S FOR ALL ORGANS EXCEPT SKIN. PHOTO% P L t l ELECTRON C DOSE-RATE FACTORS FOR SKIN. AN0 EFFECTIVE (MSE-RATE FACTGRS FOP TMBEE C EXPOSURE NODES C a

C A I R Ib;MERSIOi1 6 C

1 WRITE (15.41 !M!CLs THALFm ( W S O R G I l e J J r J-109) 4 FORHAT ( I H tA+. 1X. 3A4. 9 I l P E l 1 - 2 I 1

WPITE ( 1 6 0 4 ) ItUCL. THALFI t C O S O R G ( I . J I ~ J-lO.161r (DOSOICCIeJIe

WRITE ( l l r 4 ) INUCLI THALF. t W S O R G I I ~ J I ~ J = Z 0 * 2 3 I . OOSEFFt 1s. 2 JSl8.19)

2 0 0 f O R C ( l . l ? ) r DOSU8(1 .48 . C O S S K N I I I C - C WATER IeWERStON C

WRITE I Z O e S I IMJCL. THALFI WRITE 121.4I I W C L . THALF.

2 J - I B e 1 9 I

I WSOPCt 21 JI 1 DOSORG I 2 0 JI

J- 1 e 9 I J=IO.161 e I OOSOPG (2 e J I

0 0 i) 2 4 5 . - . . ..

2 4 2

C C C

C C C C

C C C C

C C C

C

LINSKP-L!WSrP-O I F (L INSKP -Lr- WRITE (15.15l

WRITE (16r IS@ WRITE 117.L5) WRITE (20.15, WRITE (21.15t WRITE (22115J WRITE (25.15, WRITE t 2 h v l f J WRITE (27.15l

1 S FORMAT (In P

L I HSKP-0 3 LINORG-LI-8

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