research article effective atomic number...

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2013 Article ID 738978 6 pageshttpdxdoiorg1011552013738978

Research ArticleEffective Atomic Number Determination of Rare Earth Oxideswith Scattering Intensity Ratio

A TurGucu1 D Demir2 and P Oumlnder2

1 Department of Energy System Engineering Faculty of Engineering Sirnak University 73000 Sırnak Turkey2Department of Physics Faculty of Sciences Ataturk University 25240 Erzurum Turkey

Correspondence should be addressed to A Tursucu ahmettursucusirnakedutr

Received 9 July 2013 Accepted 3 October 2013

Academic Editor Borut Mavko

Copyright copy 2013 A Tursucu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Effective atomic numbers (119885eff) of scientific samples (rare earth) were determined experimentally by scattering of 5954 keV gammaphotons from 5Ci 241Amannular radioactive sourceThe scattered gamma photons were collected by using a high-resolutionHPGesemiconductor detector placed at 167∘ to the incident beam This experiment was carried out on several elements in the atomicrange 4 le 119885 le 82 for 5954 keV incident photons Photopeak efficiency and air and sample absorption corrections were performedon Rayleigh to Compton scattering intensity ratio then the ratio was plotted as a function of atomic number and a fit curve wasconstituted The effective atomic numbers of rare earth oxide samples were determined by this fit curve Also related parameterswere determined by absorption techniquewith the same incident photon energy Obtained values from this fit curvewere comparedto theoretical values and were found to closely agree with theoretical calculations

1 Introduction

Effective atomic number is an important parameter thatshould be determined for materials in composite alloy andmixture form Reliable data on the effective atomic numberswere used in radiation biology medical physics radiationdosimetry nuclear industry and space research programsAlso the effective atomic number is used for determining theX- and 120574-ray absorption fraction of materialsThere are a fewtechniques (particle induced X-ray emissions (PIXE) protoninduced gamma ray emission (PIGE) fast neutron activationanalysis (FNNA) induced coupled plasma (ICP) electricalimpedance methods XRF chemical analysis and atomicabsorption spectroscopy) to define the effective atomic num-ber of composite materials that was created by two ormore constituents One of these techniques is total photoninteraction calculation by using transmission experimentsIn addition to these techniques intensity ratio of scatteredphotons emerging from suitable sample-source and detectorarrangement was a significant experimentalmethod to deter-mine effective atomic number in a nondestructive way Thescattered intensity ratio method is regardless of density of the

sample and depends on the mixture of composite materialThe above-mentioned research techniques used in a presentstudy are subapplication of the XRF technique

Rare earth oxides of lanthanids are widely used in sci-entific industrial commercial and medical applications Forexample praseodymium oxide in solid solution with ceria orceria-zirconia is used as oxidation catalysis europium oxideis used in nuclear reactor as a neutron absorber fluorescentlamps and screening for Down syndrome and other geneticdiseases In addition to these applications terbium oxide(green phosphors in fluorescent lamps and color TV tubes)and dysprosium oxide (neutron-absorbing control rods innuclear reactors various data storage applications and inimproving the corrosion resistance of the magnets) are alsoimportant

In recent years determination of the effective atomicnumber is increasingly studied Due to the advantages mostof the investigations on this subject have been carried outusing scattering intensity ratios Singh et al [1] havemeasuredthe effective atomic numbers of scientific (lanthanide oxidesand alloys of lead and tin of known composition) andbiological samples (iodine content of tissues) using scattering

2 Science and Technology of Nuclear Installations

intensity ratio of 145 keV gamma rays Singh et al [2] havedetermined the effective atomic number of scientific samplesby scattering intensity ratio of 5954 keV gamma photonsThere are some points should be considered in the determi-nation process of the effective atomic number by scatteringintensity ratio method One of these points is thickness ofsample Increasing thicknesses are creating multiple scatter-ing centers on the target Therefore the multiple scatteringdensities are increasing with the increasing thickness Singhet al [3] have determined the effect of multiple scattering onthe effective atomic number The effective atomic number ofcomposite materials using Rayleigh to Compton scattering of279 keV gamma rays was investigated by Singh et al [4]

In this paper we have determined the effective atomicnumber of rare-earth samples by scattering intensity ratiomethod For this purpose La

2O3 Pr2O3 Eu2O3 Sm2O3 and

Er2O3rare earth samples were investigated in 167∘ scattering

angle with HPGe semiconductor detector

2 Theory

When an X-ray impinges upon a sample three things mayhappen the incident X-ray may be diffracted scatteredor absorbed Scattering will occur when an X-ray photoncollides with one of the electrons of the absorbing elementWhere this collision is elastic that is when no energy is lostin the collision process the scattering is said to be coherent(Rayleigh) scattering Since no energy change is involved thecoherently scattered radiation will retain exactly the samewavelength as the incident beamThe probability of Rayleighscattering occurrence theoretically is given as

119889120590119877

119889Ω=

1199032

0

2(1 + cos2120579) 1003816100381610038161003816119865 (119902 119885)

1003816100381610038161003816

2

(1)

where 119865(119902 119885) is the atomic form factor 119902 representing themomentum transferred to the electron 119903

0(= 28179 times

10minus15m) is the classical electron radius and 120579 is the scattering

angleCompton scattering is the interaction of a high energy

photon with an electron and the resulting ldquoscatteredrdquo photonwhich has a reduced frequency and therefore reduced energyCompton scattering requires that light is viewed as a particleand not just a wave because it is the ldquocollisionrdquo of thephoton with the electron and the exchange of energy whichaccounts for the shift in energyThe occurrence probability ofCompton scattering is provided by Klein-Nishina relation

(119889120590

119889Ω)

KN=

1

21199032

0(119864

1198640

)

2

(1198640

119864+

119864

1198640

minus sin2120579) (2)

where119864 and1198640are scattered and incident photon energies In

large values of the momentum transfer incoherent scatteringfunction (119878(119902 119885)) is equal to number of the atomic electronsand when momentum transfer approaches the zero 119878(119902 119885)is approaching the zero at the same time In this instance

the ratio of Rayleigh scattering cross-section to Comptonscattering cross-section is given as

119877 =(119889120590119889Ω)

119877

(119889120590119889Ω)aCprop

1003816100381610038161003816119865(119902 119885)1003816100381610038161003816

2

119878 (119902 119885) (3)

where (119889120590119889Ω)aC is the atomic Compton scattering cross-section that occurs from scattering by bound electrons Theatomic Compton scattering cross-section is given as

(119889120590

119889Ω)

aC= 119878 (119902 119885) (

119889120590

119889Ω)

KN (4)

Equation (3) represents the ratio of Rayleigh to Comptonscattering The 119877 value obtained from this equation isproportional to the atomic number of investigated materialThis proportion depends on 119865

2119878 ratio Theoretical data for

calculation of the Rayleigh to Compton cross-section fromparameters for 119865(119902 119885) and 119878(119902 119885) was created by Hubbellet al [5]

The 119877 value which is directly related to the atomicnumber of elemental interest is calculated via weighting ofthe atomic percentages of elements using atomic form factorand incoherent scattering function

119877 =(119889120590119889Ω)

119877

(119889120590119889Ω)aCprop

sum119899

119895=1119886at119895

10038161003816100381610038161003816119865 (119902 119885

119895)10038161003816100381610038161003816

2

sum119899

119895=1119886at119895119878 (119902 119885

119895)

(5)

here 119886at119895represents the atomic percentages and is calculated

by119882119895and the atomic mass 119860

119895of the 119895th element as

119886at119895=

(119882119895119860119895)

sum119895(119882119895119860119895)

(6)

The effective atomic number of material is calculated via theratio of its atomic cross-section to electronic cross-section

119885119890=

120590119905

120590119890

(7)

The atomic cross-section (120590119905119886) is calculated as

120590119905119886

=120583119898119873

119873119860

(8)

where 120583119898119873 and119873

119860represent mass attenuation coefficient

Avogadrorsquos number and atomic weight respectively [6] Thetotal electronic cross-section for interest element is given asfollows

120590119905119890

=1

119873sum

119895

119886119895119860119895

119885119895

(120583

120588) (9)

here 119886119895is the number of atoms of element 119895 relative to the

total number of atoms of all elements in themixture119885119895is the

atomic number of the 119895th element in a molecule and (120583120588)119895

is the total mass attenuation coefficient of the 119895th element ina molecule [4]

Science and Technology of Nuclear Installations 3

Target

Source Source

Pb shield Pb shield

HPG

e det

ecto

r

Sample chamber

Figure 1 Experimental setup

3 Experimental Setup andPresent Measurements

In this study firstly wewere aimed to determine the scatteringintensity ratios of scientific samples to obtain their effectiveatomic numbers For this purpose we used 5Ci 241Amannu-lar source as an exciter and HPGe semiconductor detectorto collect the scattering photons The HPGe detector was aDSG planar high purity germanium crystal with a diameterof 16mm a length of 10mm a berylliumwindow of 012mmand active area of 200mm2 The schematic arrangement ofthe experimental setup used in the present study is shownin Figures 1 and 2 A bias voltage of minus1500V was applied tothe detector with a resolution of 182 eV at 59 keV The rare-earth samples of thickness ranging from 0189 to 0265 gcm2were used In this study the study samples were La

2O3

Pr2O3 Eu2O3 Sm2O3 and Er

2O3 Spectrum of samples

was processed by using a Canberra (AccuSpec) Pc-basedmultichannel analyzer card For the best counting rates fromdetectorwe set the time constant ofOrtecmodel 472 amplifierat 6 120583s Operating parameters of the system were governedand controlled by the computer program Genie-2000 Thedata were collected into 1024 channels of the MCA Datawere analyzed by the Origin 75 software program A typicalspectrum of La

2O3target is shown in Figure 3 Also a typical

spectrum of V (pure vanadium) target is shown in Figure 4

4 Result and Discussion

This experiment represents a procedure to determine effec-tive atomic number of rare earth through measurementsof Rayleigh and Compton scattering intensity using photonenergy of 5954 keVThe119885eff values of rare earth were neededto be determined precisely because of their applicationsespecially in space physics nuclear physics medical physicsradioisotope monitoring neutron capturing lasers scatter-ing and attenuation of radiation testing of multicomponent

DetectorPb shield

Sample holderSample chamber

Ba reference sample Source

a

b

c

d e

Figure 2 Sample chamber (119886 = 65 cm 119887 = 63 cm 119888 = 135 cm 119889 =11 cm 119890 = 5 cm)

Cou

nts

chan

nel

12000

10000

8000

6000

4000

2000

0

700 750 800 850 900 950 1000

Compton peak

Coherent peak

Channel

Figure 3 Typical observed spectra at 167∘ from La2O3target when

irradiated by 5954 keV incident photon energy

Channel

Compton

CoherentChan

nelc

ount

32

28

24

20

16

12

00

690 720 750 780 810 840 870 900 930 960 990 1020

08

04

times104

Figure 4 A typical Compton and coherent scattering spectrumfrom pure Vanadium Target


designs of radiation shielding calculations of absorbed dosein radiotherapy and many other radioactive applications

In the present measurements a target of known atomicnumber (Be C Al Si Ca Ti V Fe Co Ni Cu Zn Y ZrNb Mo Ru Rh Pd Ag Cd Sn La Dy Yb Ta Au and Pb)and thickness (0022ndash0865 gcm2) was used The scatteredspectra of the targets are recorded for a period of 3600ndash61200 s The background was recorded after removing thetarget out of the primary beam to permit the registrationof events due to cosmic rays and to any other processindependent of the target The background count rate wassubtracted from measurements In the recorded scatteredspectra Rayleigh and Compton peaks were not simple Theywere with superimposed continuum hence the followingformula was used to subtract the additional unwanted countsincluded in this process

Peak area =

119861

sum

119894=119860

119862119894minus (119861 minus 119860)

119862119860+ 119862119861

2 (10)

where119860 and119861 are the channel numbers specifying the regionof observed Photopeak 119862

119860and 119862

119861are the counts at the

respective channels and119862119894is the simple integration of counts

between the limits 119860 minus 119861 These observed intensities werecorrected for Photopeak efficiency of the HPGe detectorabsorption in the air between target and the detector and self-absorption in the primary target as per the relation

119873actual =119873obs

120576120574120573120574119886120573120574119905

(11)

here 119873obs is the observed intensity under the Rayleigh (orCompton) peak 120573

120574119886is the correction factor for absorption of

photons in the air present between the target and the detector120573120574119905is the self-absorption correction factor for the scattered

photons in the target 120576120574is the Photopeak efficiency of the

detector for Rayleigh (or Compton) scattered photons Theself-absorption correction factor was determined using thework of Weyrich [7]

120573 =1 minus exp [minus (120583

1+ 1205832) 119889]

(1205831+ 1205832) 119889

(12)

here 1205831and 120583

2represent the absorption coefficients of

incident and scattered photons respectively and 119889 is thesample thickness

The Photopeak efficiency curve for the HPGe detectoris shown in Figure 5 and created experimentally 1381ndash121295 keV photon energy by using Am241 Ba133 Cs137 andEu152 Each of these radioactive sources of known activitywas placed at the position of the elemental target and theenergy spectra were recorded by theHPGe detectorThe solidangle subtended by the detector at the centre of the source isthus the same as in the actual measurements For a gammaemitted from a radioisotope source with a known activity theefficiency is given by the expression

120576120574=

119860119888

1198730119901120574119890minus120582119905

(13)

Effici

ency

(120576)

10 100 1000

y = minus87905 + 799653x minus 342096x2 + 036008x3

r2 = 099648

Energy (keV)

1E minus 4

1E minus 5

1E minus 6

Figure 5 The photopeak efficiency curve for HPGe detector

Rayl

eigh

to C

ompt

on in

tens

ity ra

tio

21

14

07

0

0 20 40 60 80

Atomic number

R = 005441 minus 001043Z + 39937 times 10minus4Z2

r2 = 095

Figure 6 Rayleigh to Compton scattered intensity ratio as afunction of atomic number

where 119860119888is net peak area in counts 119873

0is the activity of

source at the time of standardization 119901120574is the absolute

gamma ray emission probability 120582 is the decay constant and119905 is the elapsed time since standardization The energies andemission probabilities of the sources used in the present workwere taken from Table of Radioactive Isotopes [8]

The intensity ratio of Rayleigh and Compton scatteredpeaks for different targets of known atomic number is plottedas a function of atomic number and is given in Figure 6 Inthis figure due to lack of the same features (size thickness)of the target samples some deviations occurred in the atomicrange 40 le 119885 le 50 The solid curve represents the best-fitcurve through experimental data points corresponding to theintensity ratio of Rayleigh to Compton scattering in Figure 6[9] The equation for the best-fit curve is

119877 = 005441 minus 001043119885 + 39937 times 10minus41198852 (14)

Each of the rare earth samples is replaced with theelemental target and the scattered spectra are recordedThe intensities under the observed Rayleigh and Comptonpeaks were evaluated The use of (11) provides the actual


Table 1 Rayleigh to Compton scattered intensity ratio and experimental and theoretical effective atomic numbers of rare earth oxides at5954 keV

Rare earth Rayleigh to Compton intensity ratio Experimental effective atomic number Other experimental TheoreticalLa2O3 0535 plusmn 0002 5014 plusmn 076 mdash 5579Pr2O3 0801 plusmn 0002 5822 plusmn 074 minus5511lowast 5785Sm2O3 0978 plusmn 0002 6289 plusmn 081 mdash 6091Eu2O3 104 plusmn 0002 6515 plusmn 094 minus5888lowast 6189Er2O3 121 plusmn 0003 6841 plusmn 122 mdash 6721lowastSingh et al [1]

intensities under these peaks originating from interactions of5954 keV photons with the target atoms (electrons) and thescattered photons traveling in direction of the detector Theeffective atomic number of La


Er2O3is then deduced from the best-fit curve of Figure 6

Also the effective atomic numbers of these samples weretheoretically evaluated from known elemental concentrationof the constituent elements using mixture rule and WinX-Com program [10] The present effective atomic numbersother experimental values in the literature and Rayleighto Compton scattered intensity ratios are given in Table 1Also theoretical values of the effective atomic numbers ofrare earth are given in Table 1 The overall error in theexperimental parameters was the sum of the uncertainties indifferent factors namely the evaluation of peak areas (169ndash371) target mass thickness (145ndash320) the Photopeakefficiency (110ndash204) and statistical error (lt100) Totalerrors affecting the experimental parameters were calculatedbetween 268 and 540 Theoretical calculations do nottake into account molecular and solid-state effects XCOMdatabase neglects a strong interaction between atoms andCoulomb interaction between the photoelectron and thepositively charged ion Also database does not calculateenergy absorption coefficients This situation can be a reasonto discrepancy between theoretical and experimental values

It was clearly seen that the experimental measured valueswere in good agreement with calculated theoretical valuesAlso the present measurements showed the usability of thisexperimental technique to measure effective atomic numberTo obtain more definite conclusions on the effective atomicnumber using this method more experimental data areclearly needed particularly for different scattering angles andchemical compounds

5 Conclusion

There are many articles about determining the effectiveatomic number of composite materials Some of these articlesare related with mass attenuation technique We have pre-sented the effective atomic number of some rare earth withscattering intensity ratio For this purpose La

2O3 Pr2O3

Eu2O3 Sm2O3 and Er

2O3rare earth samples were inves-

tigated in 167∘ scattering angle with HPGe semiconductordetector Our calculations include sample air attenuationcorrection and detectors photopeak efficiency

Highlights

(i) The effective atomic number of composite material isan important parameter

(ii) Scattering intensity ratio is a significant technique todetermine effective atomic numbers

(iii) Our present experimental values in good agreementwith theory and other experimental

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M P Singh A Sharma B Singh and B S Sandhu ldquoNon-destructive evaluation of scientific and biological samples byscattering of 145 keV gamma raysrdquo Radiation Measurementsvol 45 no 8 pp 960ndash965 2010

[2] M P Singh A Sharma B Singh and B S Sandhu ldquoA non-destructive technique for assigning effective atomic number toscientific samples by scattering of 5954 keV gamma photonsrdquoNuclear Instruments andMethods in Physics Research A vol 619no 1ndash3 pp 63ndash66 2010

[3] M Singh B Singh and B S Sandhu ldquoInvestigations ofmultiplescattering of 320 keV 120574 rays a new technique for assigningeffective atomic number to compositematerialrdquo Physica Scriptavol 79 no 3 Article ID 035101 8 pages 2009

[4] M P Singh B S Sandhu and B Singh ldquoMeasurement of theeffective atomic number of composite materials using Rayleighto Compton scattering of 279 keV gamma raysrdquo Physica Scriptavol 76 no 4 pp 281ndash286 2007

[5] J H Hubbell E H Veigele R T Briggs D T Brown R JCromer and J Howertan ldquoAtomic form factors Incoherentscattering functions and photon scattering cross sectionsrdquoJournal of Physical and Chemical Reference Data vol 4 pp 471ndash538 1975

[6] D C Wang P Luo and H Yang ldquoMeasurement of the massattenuation coefficients for SiH

4and Sirdquo Nuclear Instruments

and Methods in Physics Research B vol 95 no 2 pp 161ndash1651995

[7] W Weyrich ldquoThe electron momentum distribution in solidpotassiumfluoride studied by compton scatteringrdquoBerichte derBunsengesellschaft fur Physikalische Chemie vol 79 no 11 pp1085ndash1095 1975


[8] R B Firestone and L P Ekstrom WWW Table of RadioactiveIsotopes version 21 January 2004 httpielblgovtoi

[9] D Demir andA Tursucu ldquoMeasurement of the effective atomicnumber of Fe

119909Cr1minus119909

and Fe119909Ni119909alloys using scattering of

gamma raysrdquo Journal of Alloys andCompounds vol 581 pp 213ndash216 2013

[10] L Gerward N Guilbert K B Jensen and H Levring ldquoX-rayabsorption in matter Reengineering XCOMrdquo Radiation Physicsand Chemistry vol 60 no 1-2 pp 23ndash24 2001

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intensity ratio of 145 keV gamma rays Singh et al [2] havedetermined the effective atomic number of scientific samplesby scattering intensity ratio of 5954 keV gamma photonsThere are some points should be considered in the determi-nation process of the effective atomic number by scatteringintensity ratio method One of these points is thickness ofsample Increasing thicknesses are creating multiple scatter-ing centers on the target Therefore the multiple scatteringdensities are increasing with the increasing thickness Singhet al [3] have determined the effect of multiple scattering onthe effective atomic number The effective atomic number ofcomposite materials using Rayleigh to Compton scattering of279 keV gamma rays was investigated by Singh et al [4]

In this paper we have determined the effective atomicnumber of rare-earth samples by scattering intensity ratiomethod For this purpose La


Er2O3rare earth samples were investigated in 167∘ scattering

angle with HPGe semiconductor detector

2 Theory

When an X-ray impinges upon a sample three things mayhappen the incident X-ray may be diffracted scatteredor absorbed Scattering will occur when an X-ray photoncollides with one of the electrons of the absorbing elementWhere this collision is elastic that is when no energy is lostin the collision process the scattering is said to be coherent(Rayleigh) scattering Since no energy change is involved thecoherently scattered radiation will retain exactly the samewavelength as the incident beamThe probability of Rayleighscattering occurrence theoretically is given as

119889120590119877

119889Ω=

1199032

0

2(1 + cos2120579) 1003816100381610038161003816119865 (119902 119885)

1003816100381610038161003816

2

(1)

where 119865(119902 119885) is the atomic form factor 119902 representing themomentum transferred to the electron 119903

0(= 28179 times

10minus15m) is the classical electron radius and 120579 is the scattering

angleCompton scattering is the interaction of a high energy

photon with an electron and the resulting ldquoscatteredrdquo photonwhich has a reduced frequency and therefore reduced energyCompton scattering requires that light is viewed as a particleand not just a wave because it is the ldquocollisionrdquo of thephoton with the electron and the exchange of energy whichaccounts for the shift in energyThe occurrence probability ofCompton scattering is provided by Klein-Nishina relation

(119889120590

119889Ω)

KN=

1

21199032

0(119864

1198640

)

2

(1198640

119864+

119864

1198640

minus sin2120579) (2)

where119864 and1198640are scattered and incident photon energies In

large values of the momentum transfer incoherent scatteringfunction (119878(119902 119885)) is equal to number of the atomic electronsand when momentum transfer approaches the zero 119878(119902 119885)is approaching the zero at the same time In this instance

the ratio of Rayleigh scattering cross-section to Comptonscattering cross-section is given as

119877 =(119889120590119889Ω)

119877

(119889120590119889Ω)aCprop

1003816100381610038161003816119865(119902 119885)1003816100381610038161003816

2

119878 (119902 119885) (3)

where (119889120590119889Ω)aC is the atomic Compton scattering cross-section that occurs from scattering by bound electrons Theatomic Compton scattering cross-section is given as

(119889120590

119889Ω)

aC= 119878 (119902 119885) (

119889120590

119889Ω)

KN (4)

Equation (3) represents the ratio of Rayleigh to Comptonscattering The 119877 value obtained from this equation isproportional to the atomic number of investigated materialThis proportion depends on 119865

2119878 ratio Theoretical data for

calculation of the Rayleigh to Compton cross-section fromparameters for 119865(119902 119885) and 119878(119902 119885) was created by Hubbellet al [5]

The 119877 value which is directly related to the atomicnumber of elemental interest is calculated via weighting ofthe atomic percentages of elements using atomic form factorand incoherent scattering function

119877 =(119889120590119889Ω)

119877

(119889120590119889Ω)aCprop

sum119899

119895=1119886at119895

10038161003816100381610038161003816119865 (119902 119885

119895)10038161003816100381610038161003816

2

sum119899

119895=1119886at119895119878 (119902 119885

119895)

(5)

here 119886at119895represents the atomic percentages and is calculated

by119882119895and the atomic mass 119860

119895of the 119895th element as

119886at119895=

(119882119895119860119895)

sum119895(119882119895119860119895)

(6)

The effective atomic number of material is calculated via theratio of its atomic cross-section to electronic cross-section

119885119890=

120590119905

120590119890

(7)

The atomic cross-section (120590119905119886) is calculated as

120590119905119886

=120583119898119873

119873119860

(8)

where 120583119898119873 and119873

119860represent mass attenuation coefficient

Avogadrorsquos number and atomic weight respectively [6] Thetotal electronic cross-section for interest element is given asfollows

120590119905119890

=1

119873sum

119895

119886119895119860119895

119885119895

(120583

120588) (9)

here 119886119895is the number of atoms of element 119895 relative to the

total number of atoms of all elements in themixture119885119895is the

atomic number of the 119895th element in a molecule and (120583120588)119895

is the total mass attenuation coefficient of the 119895th element ina molecule [4]


Target

Source Source

Pb shield Pb shield

HPG

e det

ecto

r

Sample chamber




2O3








DetectorPb shield



a

b

c

d e


Cou

nts

chan

nel

12000

10000

8000

6000

4000

2000

0

700 750 800 850 900 950 1000

Compton peak

Coherent peak

Channel



Channel

Compton

CoherentChan

nelc

ount

32

28

24

20

16

12

00

690 720 750 780 810 840 870 900 930 960 990 1020

08

04

times104





Peak area =

119861

sum

119894=119860

119862119894minus (119861 minus 119860)

119862119860+ 119862119861

2 (10)


119860and 119862




119873actual =119873obs

120576120574120573120574119886120573120574119905

(11)






120573 =1 minus exp [minus (120583

1+ 1205832) 119889]

(1205831+ 1205832) 119889

(12)

here 1205831and 120583




120576120574=

119860119888

1198730119901120574119890minus120582119905

(13)

Effici

ency

(120576)

10 100 1000

y = minus87905 + 799653x minus 342096x2 + 036008x3

r2 = 099648

Energy (keV)

1E minus 4

1E minus 5

1E minus 6


Rayl

eigh

to C

ompt

on in

tens

ity ra

tio

21

14

07

0

0 20 40 60 80

Atomic number


r2 = 095



0is the activity of














5 Conclusion


2O3 Pr2O3

Eu2O3 Sm2O3 and Er



Highlights






References













119909Cr1minus119909








FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Target

Source Source

Pb shield Pb shield

HPG

e det

ecto

r

Sample chamber




2O3








DetectorPb shield



a

b

c

d e


Cou

nts

chan

nel

12000

10000

8000

6000

4000

2000

0

700 750 800 850 900 950 1000

Compton peak

Coherent peak

Channel



Channel

Compton

CoherentChan

nelc

ount

32

28

24

20

16

12

00

690 720 750 780 810 840 870 900 930 960 990 1020

08

04

times104





Peak area =

119861

sum

119894=119860

119862119894minus (119861 minus 119860)

119862119860+ 119862119861

2 (10)


119860and 119862




119873actual =119873obs

120576120574120573120574119886120573120574119905

(11)






120573 =1 minus exp [minus (120583

1+ 1205832) 119889]

(1205831+ 1205832) 119889

(12)

here 1205831and 120583




120576120574=

119860119888

1198730119901120574119890minus120582119905

(13)

Effici

ency

(120576)

10 100 1000

y = minus87905 + 799653x minus 342096x2 + 036008x3

r2 = 099648

Energy (keV)

1E minus 4

1E minus 5

1E minus 6


Rayl

eigh

to C

ompt

on in

tens

ity ra

tio

21

14

07

0

0 20 40 60 80

Atomic number


r2 = 095



0is the activity of














5 Conclusion


2O3 Pr2O3

Eu2O3 Sm2O3 and Er



Highlights






References













119909Cr1minus119909








FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















Peak area =

119861

sum

119894=119860

119862119894minus (119861 minus 119860)

119862119860+ 119862119861

2 (10)


119860and 119862




119873actual =119873obs

120576120574120573120574119886120573120574119905

(11)






120573 =1 minus exp [minus (120583

1+ 1205832) 119889]

(1205831+ 1205832) 119889

(12)

here 1205831and 120583




120576120574=

119860119888

1198730119901120574119890minus120582119905

(13)

Effici

ency

(120576)

10 100 1000

y = minus87905 + 799653x minus 342096x2 + 036008x3

r2 = 099648

Energy (keV)

1E minus 4

1E minus 5

1E minus 6


Rayl

eigh

to C

ompt

on in

tens

ity ra

tio

21

14

07

0

0 20 40 60 80

Atomic number


r2 = 095



0is the activity of














5 Conclusion


2O3 Pr2O3

Eu2O3 Sm2O3 and Er



Highlights






References













119909Cr1minus119909








FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

























5 Conclusion


2O3 Pr2O3

Eu2O3 Sm2O3 and Er



Highlights






References













119909Cr1minus119909








FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















119909Cr1minus119909








FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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