Total bremsstrahlung spectra of thick lead compounds produced by 90Sr beta emitter in photon energy region of 10–100 keV

Total bremsstrahlung spectra of thick lead compounds produced by 90Sr beta emitter in photon energy region of 10–100 keV

Nuclear Instruments and Methods in Physics Research B 401 (2017) 33–37 Contents lists available at ScienceDirect Nuclear Instruments and Methods in ...

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Nuclear Instruments and Methods in Physics Research B 401 (2017) 33–37

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Total bremsstrahlung spectra of thick lead compounds produced by 90Sr beta emitter in photon energy region of 10–100 keV Suhansar Jit Sharma a, Tajinder Singh b,⇑, Doordarshi Singh c, Amrit Singh d, A.S. Dhaliwal e a

Department of Physics, B.B.S.B Polytechnic, Fatehgarh Sahib, Punjab, India Department of Physics, Mata Gujri College, Fatehgarh Sahib, Punjab, India c Department of Mechanical Engineering, B.B.S.B Engineering College, Fatehgarh Sahib, Punjab, India d Department of Physics, Baba Ajay Singh Khalsa College, Gurdas Nangal, Gurdaspur, Punjab, India e Department of Physics, Sant Longowal Institute of Engineering & Technology, Longowal (Sangrur), Punjab, India b

a r t i c l e

i n f o

Article history: Received 12 February 2017 Received in revised form 3 April 2017 Accepted 6 April 2017

Keywords: Polarization bremsstrahlung Ordinary bremsstrahlung Lead compounds Beta emitter

a b s t r a c t The total bremsstrahlung spectra in the thick targets of lead acetate trihydrate (Pb(CH3COO)23H2O), lead nitrate Pb(NO3)2 and lead chloride (PbCl2) produced by 90Sr beta particles have been investigated in the photon energy region of 10–100 keV. The experimental bremsstrahlung spectra have been compared with the theoretical models Elwert corrected (non relativistic) Bethe Heitler theory, modified Elwert factor (relativistic) Bethe Heitler theory for ordinary bremsstrahlung and modified Elwert factor (relativistic) Bethe Heitler theory which includes polarization bremsstrahlung in the stripped atom approximation. The experimental results show better agreement with theoretical model that includes polarization bremsstrahlung in stripped approximation in the photon energy region below 30 keV. However, at higher photon energy region 30–100 keV, the theoretical model which describes ordinary bremsstrahlung is more accurate to describe the experimental bremsstrahlung spectra. The experimental results show positive deviations from the entire theoretical models at higher energy end of the spectrum. The results indicate that polarization bremsstrahlung plays important role in the formation of total bremsstrahlung spectra in lead compounds produced by continuous beta particles at low photon energy region of 10– 30 keV. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction The bremsstrahlung spectral photon distribution in thick targets of compounds is needed to be studied with continuous beta particles and mono-energetic electrons. The emission of radiation due to scattering of electrons from the static coulomb field of the target nucleus is termed as ordinary bremsstrahlung (OB), while polarization bremsstrahlung (PB) is generated due to change in dipole moment of the target atoms due to the colliding particles. Total bremsstrahlung (BS) is the sum of the OB intensity and PB intensity. OB has been investigated and reported theoretically as well as experimentally at various electron energies at different photon energies [1–5]. Amusia et al. [6] considered that PB can be added with OB in the born approximation for non relativistic electron energies using stripped approximation (SA). Avdonina and Pratt [7] calculated the total bremsstrahlung spectra (BS) in

⇑ Corresponding author. E-mail address: [email protected] (T. Singh). http://dx.doi.org/10.1016/j.nimb.2017.04.027 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.

the stripped approximation (SA). Korol and Solov’yov [8], Amusia [9] have given detailed reviews on PB studies. Quarles and Portillo [10] investigated the PB contribution in the bremsstrahlung spectral distribution of photons in gaseous targets by using mono energetic electrons and reported its existence over a wide range of photon energy. It has already been proved that PB plays a major role in the formation of total BS spectra in thick metallic targets produced by beta emitters [11–13] in the low photon energy region (1–30 keV). It has also been observed that PB contribution decreases with increase in photon energy. An extensive study of literature on bremsstrahlung studies reveals that there are very few bremsstrahlung studies in thick targets of compounds as compared to thick metallic targets. In literature, there is no study available that included the contribution of PB in the formation of BS spectra in compounds which plays an important role at lower photon energies. Manjunatha and Rudraswamy [14] evaluated the OB cross section of detector compounds by using OB cross section data of constituent elements using Langrange’s interpolation method and formula for modified atomic number Zmod given by Markowicz

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[15]. Manjunatha and Rudraswamy [16] studied the OB spectra in PbCl2 and CdO in the photon energy range 100–700 keV by using 204 Tl beta source. They compared the experimental results with the theoretical results by using the OB cross sections tabulated by Martin and Berger [17], experimental results showed agreement with theory at lower energy and disagreement at higher energy region. Manjunatha et al. [18] also studied the OB spectra in PbCl2 and CdO compounds in the photon energy range 20–180 keV using 147 Pm beta source and observed more deviation at high energy end of spectrum. Manjunatha and Rudraswamy [19] also measured the OB yield of 90Sr-90Y, 147Pm and 204Tl in CdO, PbF2, Pb (NO3)2 and PbCl2 compounds with small positive deviation less than 9% in all compounds with respect to theoretical results. Further, Manjunatha and Rudraswamy [20] investigated the OB spectra in PbCl2, PbF2, Pb(NO3)2 and CdO compounds using 90Sr-90Y beta source and NaI (Tl) detector in the higher photon energy region 200– 2000 keV and compared their results with the Tseng and Pratt [3] theory. A good agreement with the theory was observed at lower energy range but positive deviation more than 10% were observed in the photon energy region above 1000 keV. In the present study total BS spectra in compounds of lead chloride [PbCl2], lead nitrate [Pb(NO3)2] and lead acetate trihydrate [Pb (CH3COO)23H2O] has been investigated in the photon energy region 10–100 keV using Si(Li) detector and 90Sr beta source. The experimental results have been compared with the theoretical results from Elwert corrected (non relativistic) Bethe Heitler theory (EBH), modified Elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for ordinary bremsstrahlung and modified Elwert factor (relativistic) Bethe Heitler theory (FmodBH + PB) which includes polarization bremsstrahlung in the stripped atom approximation. The EBH theory describes the bremsstrahlung cross sections by considering the first order born approximation along with the Elwert factor that includes the coulomb field effects of target nucleus on incident electrons and scattered electrons. This theory describes the bremsstrahlung by considering the static behaviour of target nucleus only. Fmod BH theory replaces the relativistic velocity by relativistic momentum in EBH theory and describes the OB cross sections of target atoms in higher order born approximation. FmodBH + PB theory includes the contribution of PB into OB in the total BS spectral distribution by using stripped atom approximation which is very important in the low energy region. In this work the efforts were made to study the role of PB in the formation of BS spectra in compounds at different photon energies. The study will help to reveal the accuracy of BS theory that involves PB in the formation of BS spectra in compounds. Moreover, most of the studies in compounds have been done for higher photon energy i.e., greater than 100 keV. In the low energy region the BS studies are required with high resolution detector to critically check the accuracy of BS theories in the lower photon energy range 10–100 keV. In the lower photon energy region the processes of backscattering, absorption of photons by thick targets and detector elements etc. play a major role in the BS spectra and is needed to include for evaluation of BS spectra. In the present case the modified atomic number (Zmod) of compounds has been evaluated from formula by Markowicz [15]. The formula is

Pl wi z2i Zmod ¼

i Ai Pl wi zi i Ai

ð1Þ

Here, Wi is the weight fraction, Zi is the atomic number and Ai is the atomic weight of ith element in the compound. The results of Shivaramu [21] found that Zmod to be in better agreement with the experiment as compared to mean atomic

number Zmean. Semaan and Quarles [22] modified the Bethe Heitler formula [1] by including the back scattering factor. The expression for bremsstrahlung spectral distribution ½ncor ðW 0e ; k; ZÞ in a thick target that can be applied to thick compound targets is as

Z

ncor ðW 0e ; k; Z mod Þ ¼ RN

W 0e 1þk

drðW e ; k; Z mod Þ=dk dW e ðdW e =dxÞ

ð2Þ

Here R is the backscattering factor, given as



1  gðW e ; Z mod Þ

ð3Þ

1  gðW e ; Z mod Þ Wk 2 2

e

where, We = 0.4 Wmax (Wmax is the end point energy of beta source),

gðW e ; Z mod Þ is total back scattering factor, -dWe/dx is the stopping

power of electrons and that can be obtained from Berger and Seltzer [23] The BS spectral photon distribution, in terms of number of photons of energy k per unit mo c2 per beta disintegration, for continuous beta particle, is given by S(k,Zmod)

Z Sðk; Z mod Þ ¼

W max

1þk

0

ncor ðW 0e ; k; Z mod ÞPðW 0e ÞdW e

ð4Þ

0

Here PðW 0e ÞdW e is the beta spectrum of the beta emitter under study. In the present study beta spectrum is obtained from Laslett et al. [24] At lower photon energy, the absorption of photons by target and detector elements becomes significant and can’t be neglected. T. Singh [25] has applied these corrections successfully in his studies on BS spectra on thick metallic targets. The corrected S(k, Z) is given by

Scor ðk; Z mod Þ ¼ nðkÞSðk; Z mod Þ expðþlx0 Þ

ð5Þ

Here, n(k) is detector efficiency x0 = x  R0, where, ‘x’ is the thickness of target in units of mg/cm2 and ‘xo’ is the optimum thickness of the target and R0 is the mean range for the given target and is given by Evan [26]. The values of mass attenuation coefficients l for different compounds can be obtained from the tabulation of Chantler et al. [27]. The BS photon yield T for the target, with kmin and kmax as the lower and upper limit of photon energy of the BS spectrum respectively is given by

Z T¼

kmax

Scor ðk; Z mod Þdk

ð6Þ

kmin

Computer programs were written to calculate the theoretical BS spectra in terms of number of photons of energy k per unit m0 c2 i.e. Scor ðK; Z mod Þ. The experimental results were compared with theoretical models of OB and theoretical models containing PB in the formation of BS spectra. Theoretical and experimental results were compared in terms of number of photons of energy k per unit m0 c2 per unit total photon yield Scor ðK; Z mod Þ=T in order to remove the uncertainty of the source strength. 2. Experimental details The geometrical set up for measurements of total bremsstrahlung spectral photon distributions in thick targets of compounds by using Si (Li) detector was prepared as shown in Fig. 1. Si (Li) detector with resolution of 155 eV at 5.9 keV and high detecting efficiency is used for the present measurements. The background effect is reduced by using lead bricks of thickness 3 cm wrapped in Al foils around the source and target arrangement. A Perspex beta stopper technique has been used in the present investigation

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8

POSITION B

4

12

1

2 3

5

11 10

7

6

POSITION A

9 Fig. 1. Experimental set up: 1) lead shielding(30 mm) 2) beta source 3) source stand 4) Perspex sheet 5) source holder 6) Perspex holder position 7) Be window (25 lm, diameter 10 mm) 8) lead collimation (diameter 10.1 mm, length 10 mm) 9) working axis 10) detector collimation 11) Pre Amplifier 12) Si (Li) chip. Position A: target facing the source, Position B: target facing the detector.

1010

PbCH3COO PbNO3 PbCl2

109

No. of Photons Of Energy k per unit m0c2

to remove the contribution of internal bremsstrahlung (IB), bremsstrahlung generated in the source material and room background. Targets of Pb (CH3COO)23H2O (202.5 mg/cm2), Pb(NO3)2 (215 mg/cm2), PbCl2 (200 mg/cm2) has been used in the present studies. Initially calibration of spectrometer was done by using gamma sources then two sets of observations were taken for a time interval of 150,000 s at position A and position B (Fig. 3.1). The difference of photon spectral distribution from these two positions eliminates the contributions of IB, room background, bremsstrahlung generated in the source material, characteristics X-rays, if any, from these measurements. Statistical accuracy of the data was better than 1% in the 10– 100 keV range for all the compound targets as the measurement was taken for long time period of 150,000 s. The true spectrum from the experimental measured bremsstrahlung spectra of Pb (CH3COO)23H2O, Pb(NO3)2 and PbCl2 thick targets was obtained by applying various corrections i.e., self absorption of photons in target, detector elements and Perspex, backscattering of electrons and geometrical efficiency of detector. The geometrical full energy peak detector efficiency of Si (Li) detector was obtained from intrinsic efficiency and photo fraction values of detector at different energies. The bremsstrahlung photon spectral distribution was converted to number of photons of energy k per unit m0 c2 by dividing measured photon spectral distribution by common channel width and by geometrical full-energy peak detection efficiency of detector. The experimental results in terms of number of photons of energy k per unit m0 c2 for PbCl2, Pb (CH3COO)23H2O and Pb(NO3)2 thick targets for 90Sr beta particles in the photon energy region of 10 keV to 100 keV are shown in Fig. 2. Total photon yield can be obtained by graphical integrating the spectrum in the given energy range of 10–100 keV. Finally, the corrected true experimental bremsstrahlung spectral photon distributions were converted into the number of photons of energy k per unit mo c2 per unit total photon yield by dividing them by the total photon yields in the different target materials and plotted against the photon energy k.

108 107 106 105 104 103 102 101

20

40

60

80

100

Photon Energy keV Fig. 2. Number of photons of energy k per m0c2 per unit total photon yield versus photon energy (keV).

3. Errors The errors in full energy detection efficiency of detector, backscattering, counting statistics and attenuation of generated photons in the target materials contribute in the present

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Fig. 3(a) and (b) shows the comparison of Scor(k,Z)/T between theory and experiment for Pb (CH3COO)23H2O The experimental data is in agreement with the Fmod BH + PB theory within 13% up to 22 keV, beyond this energy the experimental values are close to Fmod BH theory. The deviation of experimental data from FmodBH theory varies from 14% at 23 keV to 41% at 47 keV. The PB contribution is found to decrease from 13% at 10 keV to 1% at 25 keV photon energy. From fig. 3(c) and (d) it is clear that in case of lead nitrate the experiment is in agreement with the Fmod BH + PB theory within 14% up to 24 keV. The experimental results get closer to Fmod BH theory beyond 30 keV. The deviations from Fmod BH theory is 14%, 29% and 44% at 30 keV, 50 keV and 100 keV respectively. The PB contribution is found to decrease with increase in photon energy from 27% to 1% at 10 keV and 25 keV respectively. Fig 3(e) and (f) shows the BS photon spectral distribution for PbCl2 compound target. The experimental data is in agreement with Fmod BH + PB theory within 15% at 27 keV beyond this energy the experimental values becomes more closer to Fmod BH theory it deviates from Fmod BH theory by 18%, 23% and 38% at 25 keV, 50 keV and 100 keV respectively. The PB contribution in this compound varies from 35% to 1% at 10 keV to 30 keV.

investigation. The statistical accuracy was better than 1% in the entire energy region as the measurement was taken for a long time of 1,50,000 s. The uncertainties in the photo-fraction values are 2% makes sure the uncertainty in the geometrical full energy peak detector efficiency to be less than 3%. The errors in attenuation coefficients of compound targets, Perspex, air and detector elements were less than 1% except near the edges where uncertainties are high as reported by Chantler et al. [27]. The uncertainties in the values of the electron backscattering factor R were less than 1%. The overall estimated error in the present investigation is less than 10%. 4. Results and discussion The bremsstrahlung spectral photon distribution has been studied experimentally and theoretically in Pb(CH3COO)23H2O, Pb (NO3)2, PbCl2 compounds in the photon energy region of 10– 100 keV. The experimental measurements have been compared with EBH, Fmod BH theories for OB and Fmod BH + PB theory which includes PB in SA. The results are compared in terms of number of photons of energy k per m0 c2 per unit total photon yield Scor ðK; Z mod Þ=T . -3

(b) 10

(a)

(c)

100

100

Lead Nitrate

Lead Acetate Trihydrate

Lead Acetate Trihydrate Experiment

Experiment

10-1

Experiment -1

10

EBH

10-4

EBH

10

FmodBH

10-2

FmodBH EBH FmodBH+PB

Scor(k,Zmod)/T

-2

Scor(k,Zmod)/T

Scor(k,Zmod)/T

FmodBH+PB

FmodBH+PB FmodBH

10-3

10-5

10-3 10-4

10-4 10

15

20

25

30

30

40

50

60

70

80

90

100

10

Photon Energy keV

Photon Energy keV

(e)

(d)

20

25

30

Photon Energy keV

100

(f)

Lead Chloride

Lead Nitrate

15

Lead Chloride

10-5

Experiment

10-1

Experiment

Experiment

FmodBH+PB

-4

10

-6

10

10-2

FmodBH

FmodBH

EBH

10-3

Scor(k,Zmod)/T

EBH

Scor(k,Zmod)/T

Scor(k,Zmod)/T

FmodBH+PB

10-4

-5

10

FmodBH

10-7

EBH FmodBH+PB

-8

10 10-5

10-9

10-6

10-6

10-7

30

40

50

60

70

80

Photon Energy keV

90

100

10

15

20

25

Photon Energy keV

30

10-10

30

40

50

60

70

80

90

100

Photon Energy keV

Fig. 3. [a-f] Number of photons of energy k per m0c2 per unit total photon yield versus photon energy (keV) (Errors are lying within the experimental points).

S.J. Sharma et al. / Nuclear Instruments and Methods in Physics Research B 401 (2017) 33–37

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It is clear that there is a continuous decrease of PB in the BS spectra with the increase in photon energy and PB increases with the increase in modified atomic number (Zmod) of thick compound targets. In the lower photon energy region FmodBH + PB theory is more accurate to describe the experimental results. However, at higher photon energies the curve representing FmodBH + PB theory is lower than Fmod BH theory because of the screening effects and interference effects that are neglected in calculating the BS spectral distribution in FmodBH + PB theory by using stripped approximation. In the case of thick compound targets, the multiple scattering and interatomic correlations effects also plays significant role in suppression of PB with increase in photon energy. The experimental data reported in the present measurement shows more deviations from OB theories as compared to the results reported by Manjunatha et al. [18]. Manjunatha et al. [18] reported the bremsstrahlung spectra in thick targets of compounds PbCl2 and CdO in the photon energy region of 20–180 keV by using NaI (Tl) detector. The experimental results had been compared with Tseng and Pratt theory [4] for OB. However, the contribution of PB into OB in BS spectral distribution is neglected in the investigation which is very important in the low photon energy region. Moreover, the results reported in the present measurement is more accurate as the data has been taken with the Si(Li) detector which has better energy resolution and higher detecting efficiency than NaI(Tl) detector in the photon energy region of 10–100 keV. The experimental BS spectral distributions have been corrected by applying various corrections such as electron backscattering, absorption of photons in the target and range of beta particles that probably ignored by the previous studies [14,16,18].

Fmod BH theory because of the screening contributions of the surrounding electrons of target atoms which are neglected by PB theory in stripped approximation. Further, it has been observed that low Z elements present in the compounds suppress the dominance of PB in total BS spectra. At lower energies the factors like multiple scattering, interference of OB and PB, Isotropy effects also play an important role. These factors should also be considered in the theory to improve the accuracy of the theory. More studies are required in various compounds to study the role of polarization bremsstrahlung in the formation of total bremsstrahlung spectra.

5. Conclusions

[19]

It can be concluded from the above discussion that Fmod BH + PB theory is effective to study the total BS spectra in lead acetate trihydrate, lead nitrate and lead chloride compounds up to 22 keV, 24 keV and 27 keV photon energies respectively. In the higher photon energy region i.e. above 30 keV the results are closer to FmodBH theory and as the photon energy increases the deviation of experimental data from this theory increases. It can be concluded that PB contribution decreases with increase in photon energy in compounds. At higher energies the experimental results get closer to

[20] [21] [22] [23]

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