Pertanika 15(1), 55-59 (1992)

Calculation of the Effective Stopping Powerof Ions Generated by Neutrons in Tissue Constituents

ELIAS SAlONDepartment ofPhysics

Faculty ofScience and Environmental StudiesUniversiti Pertanian Malaysia

43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

D.E. WAITDirector and Safety Advisor

Environmental Health and Safety ServicesUniversity ofSt. Andrews

St. Andrews, Fife, KY16 9TS, United Kingdom

Key words: stopping powers, heavy charged particles, Ziegler's universal screening length.

ABSTRAK

K.ertas ini rnelaporkan pengiraan kuasa penghenti zarah-zarah bercas berat yang tersentak oleh neutron dalam empat­unsur kandungan tisu bagi tenaga zarah daripada 0.1 keY hingga 1.0 MeV. Pada tenaga rendah kurang daripada 30keVj amu yang mana proses penghenti nukleus lebih berperanan daripada proses penghenti elektron, nilai kuasa penghentiberkesan lebih tinggi daripada nilai pendekatan perlambatan selanjarnya (PPS). Sisihan di antara kedua-dua nilai inibergantung kepada jisim sasaran dan juga tenaga serta jisim zarah.

ABSTRACT

This paper reports the calculation of stopping powers of heavy charged particles generated by neutrons in four-elementtissue constituents for particle energies from 0.1 keY to 1.0 MeV. At low projectile energies of less than 30 keVjamu wherethe nuclear stopping phenomenon is more dominant than the electronic stopping phenomenon, the effective stoppingpowervalues are higher than the continuous slowing-down approximation (CSDA) values, from which the deviation is dependentupon the target mass and the energy and mass of the projectiles.

INTRODUCTION

Knowledge of stopping powers and projectedranges of low-energy secondary charged particlesis very important for accurate prediction of en­ergy deposition by intermediate energy neutronsin tissue (AI-Affan et ai. 1984). Intermediate en­ergy neutrons slow down in tissue matter to gen­erate short-range heavy charged particle recoilswhich have ranges less than the cellular dimensionof most mammalian cells. The radiation quality ofthese neutrons, however, is not fully defined forradiation protection purposes although chargedparticles generated by these neutrons are knownto be capable of producing biological effects (lungand Zimmer 1966; AI-Kazwini et al. 1988). Somehave reported an increase in the radiobiological

effectiveness (RBE) of intermediate energy neu­trons of energies less than 100 keY (Key 1971;Mill 1986).

The penetration of charged particles throughmatter is a complex phenomenon which can bemeasured in terms of stopping power and pro­jected ranges. In the region where projectile ve­locities, v, are greater than the electronic orbitalvelocity, Vo (= 21te2j h = 25 keYjamul the pathlength of ions in matter is a straight line. How­ever, in the low energy region, i.e. v < vo' thepathlength is no longer a straight line but a com­plex form (Cook et al. 1953) due to various inter­action processes such as elastic collision with thetarget atom, inelastic collision with electrons,charge exchange and chemical binding effects. Ingeneral, there is competition between the loss of

PERTANlKA VOL. 15 NO.1, 1992 55

ELIAS SAlON & D.E. WATT

where Sn and Se are reduced nuclear and elec­tronic stopping power respectively. The reducednuclear stopping power is given by Ziegler inequations (5) and (6) for low and high energyions respectively.

(4)

(2)f(x) = 0.021 [In (m/m)F-

, J

0.1434 [In (m/m)] + 0.3642• J

Ziegler et al. (1985) introduced a new univer­sal screening length, a, = 0.8854a/ (ZiO.23 + zt23

) ,

Where Z and Z are the atomic number of recoil, J

ion type i and target atom type j respectively. Thecorresponding screening function produces a tightgrouping with a standard deviation of 18%, betterthan the one derived from a well-known Lind­hard's screening length, aL = 0.8854a/ (Zi2/3 +Z.2/3) 1/2, which has standard deviation of 40%. They

Jfound that their fitting universal screening func-tion is in good agreement with the experimentaldata within 5% of the standard deviation. The re-

duced energy, cz

' for ions of energy E (keY), in

terms of Ziegler's screening length is given by

32.53rn j E£ = --------"--------- (3

z Z.Z.(rn.+rn.)(ZO.25+ Z?25) )I J ' J 1 J

The total stopping power is the sum of the nu­clear and electronic stopping powers expressed interms of Ziegler's reduced energy by

. 8.462 x 10-15 ZjZjmj'S·(E)= x

J (m j + m j ) (Z~·25 + Zj25)

[Sn (Ez ) + Se (Ez )]

is given as

MATERIALS AND METHODS

energy of charged particles to electrons and torecoil particles (Lindhard and Scharff 1961). Theparticles undergo successive small angle scatter­ing known as multiple scattering which may pro­duce recoils deflected in the direction inside themedium, increasing the stopping cross section peratom. The scattering angle becomes larger as theparticle energy decreases. The particles travel in azig-zag path which partly explains the differencebetween the projected range and path length ofions at low energies. The difference is very signifi­cant at energies where quasi-elastic scattering be­comes dominant (Watt 1972).

The projected range is an average thicknessof material traversed by a number of particles di­rected perpendicular to the material surface. Theeffective stopping power is the energy loss per unitlength along this projected range. For low energyions the effective stopping power value is greaterthan the continuous slowing down approximation(CSDA) value because of the significant impor­tance of elastic scattering collisions with nuclei ofthe target materials and range of straggling. Inthe region where nuclear stopping becomes moredominant than electronic stopping, and experi­mental stopping-power data is lacking, the stop­ping process of charged particles in matter is notfully understood and here, -an attempt is made toinclude the effective nuclear stopping in the gen­eral stopping power formula. However, for ions athigh energies, the effective stopping power willbe the same as the CSDA stopping power becausethe loss of energy there is mainly due to collisionswith atomic electrons.

Calculation ofEffective Stopping Power

The effective stopping power, is/if (E), can be de­termined according to Watt and Sutcliffe (1972)in a manner similar to that adopted by Al-Mfan etal. (1984).

Sn(cJ_ In (1 + 1.1383 E z )

- 2[cz +0.01321E~·21226 + 0.19593°·5]

for Ez S; 30 keY/amu

(5)

Se(E,)

(1)

where E is the energy of the recoil particle, 'S/ (E)and ise (E) are the nuclear and electronic stop­ping powers of recoil particle type i in the atom

typej respectively. "(2 = 4 m; mj / (m; + m)2 with m;

and m being masses of particle i and target j re­spectiJely. f(x) is the function which converts theeffective stopping power of nuclear stopping and

In (E z )Sn (Ez)=-2-- for Cz > 30 keV/amu (6)

Cz

The corresponding reduced electronic stoppingpower can be expressed accordingly in terms ofZiegler's screening length by

)

3127.93 x10-2 Z2/3 z1I2 (m. + m. £112

I J 1 J z

(Note the occurrence of Z-<l·23 replacing Z·1/3 in the

56 PERTAN1KA. VOL. 15 NO. I, 1992

CALCUlATION OF THE EFFECTIVE STOPPING POWER OF IONS

10 '

o

N

10 '10 I

CARBON

-±--........--"t--=---c-=_"""""-; •• .. leW

10 '

x 0.01

10 'L'_~~~",,-~~~,",",,",,--~~~uL-~~~""""'"

10-1

PROJECT ILE ENERGY (kaV)

Fig. 1: The calculated effective and CSDA values of stoppingpowers for heavy ions (proton, C, Nand 0) in hydrogen

10 10

HYDROGEN

D10 '

>< 0.01 +- +

NNI

EUm'- ...>Ql

-"

C0: 10 7

ll.J::> ...0 + -0..

~~t.:JZ

>-'~ 10 •0..0..

~,eff0l-- csda([)

Rayno ld8 8' .1. () 9531•10 '

0 Fakuda 119821Vay I 11953)Oldenburg end 800z 119721

NX 0.1I

E - - - - - .-. • •u 10 7m ..

"- ••>• COJ

-t#_'f-~~-"

I I0: 10 ' :t---""'~ - - - - .J .. }-a=' ~ll.J

~M~::>00..

t.:J ....-Z a10'

~ .. ~ 0__Seff I - - - Scsda0..

0.. A Reyno ldo a' "l. 1195310 · Ph'llips 119531l--([) 0 \II) nS8arden & Duck.... orth 11962)

0 Sa, Arkhlpov and Gatt 119691

10 •SntSe, Arkhl pov Qnd Gatt (J969)Noorhoed (19651· Ormrod and Duck.....orth (19631· Hogb8rg 11971)· Fa8'rup 0' al. (19661

... Oldenburg and B002 11972110 J

10-110' 10 I 10' 10 J

the projectile energy increases. Also, the devia­tion for a given target decreases with the mass ofthe projectile. The deviation is largest for protons

PROJECTILE ENERGY (kaV)

Fig. 2: The calculated effective and CSDA values of stoppingpowers for heavy ions (proton, C, Nand 0) in carbon

RESULTS AND DISCUSSION

expression given by Watt and Sutcliffe (1972)).In the high energy region, however, the con­

tribution from nuclear stopping is very small andcan be neglected. Therefore, one needs to con­sider only the electronic stopping power and thiscan be calculated according to the Bethe formulaor by Ziegler's code (1985). The latter has beenadopted in this work.

The effective stopping powers of heavy recoilions (i.e. protons, C, N, 0) in tissue constituents(i.e. hydrogen, carbon, nitrogen and oxygen) havebeen determined. Except for recoil protons, theCSDA nuclear stopping power for C, Nand 0ions was calculated according to equations (5),(6) and the first term of equation (4). The elec­tronic stopping powers of energies of less than 30keY/amu were calculated according to equation(7) and the second term of equation (4). Thechoice of energy cut off corresponds to the ionvelocity of about 2.25 x 106 m s". The electronicstopping powers for ions in the high energy re­gion were calculated according to Ziegler's code.Normalization was performed to connect smoothlythe stopping power values below 30 keY/amu toZiegler's stopping powers for every ion interact­ing on each target.

For protons in four-element tissue constitu­ents, the CSDA stopping powers were obtained byfitting data of the International Committee onRadiation Units and Measurements (ICRU)(Berger 1986), for energies from 1 keY to 20 MeV.The fitting results produced deviation of less than1%. Consequently, the effective stopping powerof ions in four-element tissue constituen ts was cal­culated according to equation (1).

The effective and CSDA stopping power valuescalculated for recoil ions of energy from 0.1 keVto 1 MeV in hydrogen, carbon, nitrogen and oxy­gen are shown in Figs. 1, 2, 3 and 4 respectively.The effective and CSDA stopping power valuesare indicated by S If (solid lines) and S d (brokenlines) respectively~ For nitrogen and o~;gen ions,the values have been multiplied by factors of 10and 100 respectively for graphic purposes only.The results are compared with published experi­mental data as indicated on each figure. Thetheoretical calculations of Oldenburg and Booz(1972) are also shown.

The effective stopping power values, as ex­pected, are higher than the CSDA stopping powervalues. As we can see from the figures, the devia­tion at the low energy region for a given recoilincreases with the target mass and decreases as

PERTANIKA VOL. 15 NO.1, 1992 57

ELIAS SAlON & D.E. WAIT

PROJECTILE ENERGY (keV)Fig. 3: The calculated effective and CSDA values of stoppingp01ll"rs for heavy ions (proton, C, Nand 0) in nitrogen

10' r-~~~.,.,.,...-~~~~~~~TTTT-~~~'"'1

The effective stopping power is higher than theCSDA stopping power for low energy ions due toin teraction of particles through nuclear elasticscattering. The deviation for a given particle in­creases with the target mass and decreases with anincrease in the projectile energy. For a given tar­get, it decreases with the mass of the particle. Theresults can be used to predict the quality of inter­mediate energy neutrons which could show thepossibility that elastic nuclear collisions playa sig­nificant role in determining an increase in RBEfor these neutrons.

CONCLUSION

COIllponent.The experimental stopping power data for

recoil ions of low energies are generally lower thanthe present calculations due to the fact that themeasurements were performed for electronicstopping powers. In one case when the calculatednuclear components were added to the experi­mental data of Arkhipov and Gott (1969), the re­sults were consistent with the present calculationas shown in Fig. 2, for proton in carbon. Never­theless, experimental data for most heavy ions inthe low-energy region are scarce and are not suffi­cient to test the theoretical calculations. Thepresent calculations consider the contributionfrom the effective nuclear stopping power whichis otherwise not included in the experiments. Ourresults suggest the need to study the contributionof effective nuclear elastic scattering in the pen­etration of charged particles in hydrogen, carbon,nitrogen and oxygen, from which the effectivestopping powers and projected ranges can be cal­culated. Accordingly, the effective stopping powerand projected ranges in tissue and tissue equiva­lent (TE) materials can then be extracted in therecommended manner. Both quantities are im­portant in the determination of microdose spec­tra and quality of intermediate energy neutronsin the simulated tissue volume of Tissue Equiva­lent Proportional Counter (TEPC).

o

o

OXYGEN

NITROGEN

x 0.01

10 •

NI

X O. IE0 10

7 - - - - - - -em

"-> CQJ

-'"

cr: 10 •w H::>0[l.

tel +-z10 ' -" -~ Seff

[l.Scsda[l.

0f- A Royno ld. ot .l. (1953)Ul . Phillips (19531

m F.kud. (1982)10 ' + Oldenburg end B002 119721

10 •

N

"ix 0.1 -pe ri:PE

0 107 00

m"-> Crn-'" +

cr: 10' - - - - - -IIIIt1BIlI

W.

H::>0 -+[l. l'-tel - +z

ID' .- Setf[l. -.- 5[l. csda0

Royno ld. 0' ol. 11953)f- AUl . Phillips (19531

0 Fakud. (1980110' 0 Fakud. 119811

+ Oldenburg end 8002 (1972)

10'

10-1 10 ' 10 I 10 7 10 '

10'REFERENCES

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in all the targets. In the high energy region, how­ever, the deviation is negligible because the nu­clear stopping power component is very small incomparison with the electronic stopping power

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CALCULATION OF THE EFFECTIVE STOPPI:NG POWER OF IONS

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(Received 18January 1991)

PERTANlKA VOL. 15 NO.1, 1992 59