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Thick target total bremsstrahlung spectra of lead compounds in the photon energy region 1–10 keV by 90Sr beta particles
Applied Radiation and Isotopes 130 (2017) 1–6
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Thick target total bremsstrahlung spectra of lead compounds in the photon energy region 1–10 keV by 90Sr beta particles
MARK
⁎
Suhansar Jit Sharmaa,b, Tajinder Singhc, , Doordarshi Singhd, Amrit Singhe, A.S. Dhaliwalf a
I.K. Gujral Punjab Technical University, Kapurthala, India Department of Physics, B.B.S.B Polytechnic College, Fatehgarh Sahib, Punjab, India c Department of Physics, Mata Gujri College, Fatehgarh Sahib, Punjab, India d Department of Mechanical Engineering, B.B.S.B Engineering College, Fatehgarh Sahib, Punjab, India e Department of Physics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab, India f Department of Physics, Sant Longowal Institute of Engineering & Technology, Longowal (Sangrur), Punjab, India b
H I G H L I G H T S bremsstrahlung spectra in thick targets of Pb compounds by Sr in energy range 1–10 keV. • Total results show better agreement with the model which includes polarization bremsstrahlung in stripped approximation 3–10 keV. • Experimental show positive deviation in the photon energy region of 1–3 keV. • Results • Suppression of polarization bremsstrahlung has been observed due to the presence of large fraction of low Z elements. 90
A R T I C L E I N F O
A B S T R A C T
Keywords: Polarization bremsstrahlung Ordinary bremsstrahlung Lead compounds Beta particles
Total bremsstrahlung spectral photon distribution generated in thick targets of lead compounds Pb (CH3COO)2·3H2O, Pb(NO3)2 and PbCl2 by 90Sr beta particles has been investigated theoretically and experimentally in the photon energy region 1–10 keV. The experimental results are compared with the theoretical models describing ordinary bremsstrahlung and the theoretical model which includes polarization bremsstrahlung into ordinary bremsstrahlung, in stripped approximation. It is observed that the experimental results show better agreement with the model which describes bremsstrahlung in stripped approximation in the energy range 3–10 keV. However, the results show positive deviation in the photon energy region of 1–3 keV. Further, it has been found that there is a continuous decrease of polarization bremsstrahlung contribution into ordinary bremsstrahlung in the formation of total bremsstrahlung spectra with increase in photon energy. The suppression of polarization bremsstrahlung has been observed due to the presence of large fraction of low Z elements in the compounds. The results clearly indicate that polarization bremsstrahlung plays an important role in the formation of total bremsstrahlung spectra in compounds in the studied energy region.
1. Introduction The formation of total bremsstrahlung spectra in compounds is required to be studied for mono-energetic and continuous beta particles. Total bremsstrahlung amplitude (BS) is the sum of ordinary bremsstrahlung (OB) and polarization bremsstrahlung (PB). Further, the domination of either of OB or the PB in building the BS spectra in thick targets of compounds of various elements at different photon energies can be described in terms of bremsstrahlung energy spectrum. OB is produced due to the scattering of the incident charged particles in the coulomb field of the static target nuclei, whereas the PB is produced due
⁎
to the dynamic response of an atom in the external field of the incident charged particle. Amusia et al. (1985) has described that PB can be added with OB in a stripped approximation (SA) for non-relativistic electron energies, in terms of Born approximation. An equivalent method for the BS spectra in the (SA) has been given by Avdonina and Pratt (1999), which is efficient for obtaining the BS spectra for photon energies greater than the ionization potential of the outer shell electrons of the target atom. In SA, the production of PB is described by the decrease of OB due to screening of outer shell electrons which is completely compensated by additional PB produced by the same outer shell electrons.
Corresponding author. E-mail address: [email protected] (T. Singh).
http://dx.doi.org/10.1016/j.apradiso.2017.09.010 Received 24 March 2017; Received in revised form 21 August 2017; Accepted 7 September 2017 Available online 09 September 2017 0969-8043/ © 2017 Elsevier Ltd. All rights reserved.
Applied Radiation and Isotopes 130 (2017) 1–6
S.J. Sharma et al.
The importance of PB in the formation of the BS spectra in thick metallic targets by continuous beta particles in the low energy photon region has already been reported (Singh, 2016; Singh et al., 2009; Singh and Dhaliwal, 2015). Bremsstrahlung spectral photon distribution studies are rare in compound targets as compared to the metallic thick targets. Manjunatha and Umesh (2015) studied the effective atomic number of some rare earth compounds with the study of bremsstrahlung. Manjunatha and Rudraswamy (2007a) also studied OB in thick compounds by 204Tl beta emitter in the photon energy greater than 100 keV. Manjunatha and Rudraswamy (2012) measured the OB spectra of compounds of lead using 90Sr beta emitter and NaI scintillation detector in the photon energy region of 200–2000 keV. Manjunatha and Rudraswamy (2007b) evaluated the OB cross sections in compounds using lagrange interpolation method and using data of elements given by Seltzer and Berger (1986). Manjunatha et al. (2010) has studied the OB spectra in PbCl2 and CdO compounds using continuous beta particles and NaI(Tl) detector in the photon energy range 20–180 keV. An extensive study of literature on bremsstrahlung reveals that no study has been carried out to check the contribution of PB into OB in compounds in the low energy region of 1–10 keV. As PB contribution decreases with the increase in photon energy and there is maximum interference of OB and PB at low photon energy, so it will be interesting to see the role of PB in the formation of BS spectra of compounds. The factors like multiple photon scattering, anisotropy, and absorption of photons in the targets also play an important role at low photon energy. This study will be helpful to ascertain the role of these factors in the total BS spectra of compounds. In the present study, thick targets of lead compounds Pb (CH3COO)2·3H2O, Pb(NO3)2, PbCl2 with modified atomic numbers (Zmod) 42.11,50.04 and 62.95 respectively have been used. The comparison of experimental results with the theoretical models elwert corrected (non-relativistic) Bethe Heitler theory (EBH), modified elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for OB and modified elwert factor (relativistic) Bethe Heitler theory (Fmod BH+PB) which includes PB will reveal the accuracy of these theoretical models in determining the BS spectra of thick targets of lead compounds in the energy range 1–10 keV. In the present work, the modified atomic number (Zmod) of metallic compounds has been calculated from the formula given by Markowicz and VanGriken (1984). l wiz2i Ai l wz ∑i Ai i i
50
10
2
∑i
(1)
Here, Wi, Zi, Ai are weight fraction, atomic weight and atomic number of ith element in the compound. Zmod by Markowicz is found to be more accurate than mean atomic number Zmean and it was found to be in better agreement with experimental results of Shivaramu (1990). In a thick target bremsstrahlung, the contribution of the processes such as electron scattering, excitation and ionization plays a vital role. For continuous Beta particles Bethe and Heitler (1934) gave an expression for the bremsstrahlung spectral distribution n(k,W′e,Z) in a sufficiently thick target to absorb an electron of energy W′e with N atoms per unit volume. Semaan and Quarles (2001) incorporated the correction for the self absorption of bremsstrahlung photons in the target and electron backscattering are required for n(k,W′e,Z), in case of low energy thick target bremsstrahlung. The expression for bremsstrahlung spectral photon distribution in thick target of compounds is given as W′e
n cor (k,W′e,Z) = RN
∫ 1+k
dσ(We,k,Z mod)/dk d We (−dWe/dx)
Pb(CH3COO)2.3H2O
45
10
No. Of Photons Of Energy k per unit m0c
Z mod =
Fig. 1. Experimental set up for measuring the bremsstrahlung photon spectral distribution using 90Sr source 1) source holder 2) beta source 3) Perspex sheet 4) position A of target 5) position B of target 6) Be window 7) detector collimation 8) Si(Li) chip 9) lead shielding 10) Pre amplifier 11) lead collimation 12) working axis.
Pb(NO3)2 PbCl2
40
10
35
10
30
10
25
10
20
10
15
10
10
10
5
10
0
10
0
2
4
6
8
10
Photon Energy keV Fig. 2. Plot of number of photons of energy k per m0c2 per unit total photon yield versus photon energy keV.
from the different theoretical models i.e. Elwert corrected (non-relativistic) Bethe Heitler theory (EBH), modified Elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for OB and modified Elwert factor (relativistic) Bethe Heitler theory which includes PB (Fmod BH +PB) in SA, −dWe/dx is the total energy loss per unit path length of an
(2)
Here, dσ(We,k,Z mod)/dk is the singly differential cross section taken 2
Applied Radiation and Isotopes 130 (2017) 1–6
S.J. Sharma et al.
Table 1 Percentage contribution of PB into OB in lead acetate trihydrate, lead nitrate and lead chloride compounds targets in the photon energy range 1–10 keV. Photon energy
No. of photons of energy k per unit m0c2 per unit total photon yield
Target: Lead Acetate Trihydrate
EBH
FmodBH
FmodBH+PB
EXPERIMENT
PERCENTAGE CONTRIBUTION OF PB into OB
1 2 3 4 5 6 8 10 Target lead nitrate 1 2 3 4 5 6 8 10 Target lead chloride 1 2 3 4 5 6 8 10
7.01E−01 1.68E−01 3.33E−04 1.76E−10 3.05E−20 4.48E−26 2.28E−30 3.60E−33
6.70E−01 1.69E−01 3.39E−04 1.80E−10 3.14E−20 4.63E−26 2.36E−30 3.45E−33
8.80E−01 2.17E−01 4.23E−04 2.19E−10 3.76E−20 5.56E−26 2.76E−30 3.97E−33
9.70E−01 2.45E−01 4.84E−04 2.28E−10 3.95E−20 5.89E−26 2.98E−30 4.36E−33
24 22 20 18 17 17 15 15
5.70E−01 1.35E−02 6.77E−08 5.66E−14 8.72E−22 6.07E−28 2.00E−33 2.91E−36
5.50E−01 1.38E−02 6.89E−08 5.69E−14 8.97E−22 6.28E−28 1.58E−33 3.08E−36
8.65E−01 2.14E−02 1.03E−07 8.39E−14 1.32E−21 9.10E−28 2.09E−33 3.84E−36
9.62E−01 2.43E−02 1.18E−07 8.90E−14 1.42E−21 9.78E−28 3.12E−33 4.22E−36
36 35 33 32 32 31 24 20
0.46 0.00085 3.78E−11 6.72E−17 8.05E−23 9.58E−28 1.25E−35 6.13E−39
0.52 0.00107 3.84E−11 6.89E−17 2.32E−22 9.85E−28 1.54E−35 6.42E−39
0.86 0.00172 6.19E−11 1.09E−16 3.65E−22 1.54E−27 2.38E−35 9.17E−39
0.97 0.00198 7.20E−11 1.13E−16 3.79E−22 1.60E−27 2.52E−35 9.81E−39
40 38 38 37 37 36 35 35
stopping power values and unfolded beta spectrum in the programme the results were obtained for S(k,Zmod). Now, by applying the above mentioned corrections the results were obtained for Scor (k,Z mod) . The total photon yields T were obtained for different targets from graphical integration of the BS spectra from the plots of Scor (k,Z mod) versus photon energy k between kmin and kmax. Comparison of experimentally measured bremsstrahlung spectra for different targets and the theoretical results obtained from Eq. (6), are made in terms of the number of photons of energy k per m 0 c 2 per unit total photon yield versus photon energy to make the results independent of source strength and to eradicate the errors in the experimental results.
electron in a target material, which includes radiative and collision loss, these values are taken from the tabulations given by Berger and Seltzer (2000). Electron backscattering factor ‘R’ is given by
R=
1 − η(We, Z mod) 1 − η(We, Z mod)
k2
(3)
W2e
Here, We = 0.4Wmax , Wmax is the end point energy of beta particles and η(We, Z mod) is the total backscattering factor. The BS spectral photon distribution in terms of number of photons of energy k per unit m 0 c2 per beta disintegration for continuous beta particle is given by S(k, Z mod) .
2. Experimental details
Wmax
S(k,Z mod) =
∫
ηcor (W′e,k,Z mod)P(W′e)dW′e
The continuous beta particles produced from the pure beta emitter Sr of source strength 5 μCi. 90Sr undergoes decay into 90Y emits beta particles with end point energy of 546 keV. Further, 90Y undergoes decays to 90Zr with emission of beta particles having end point energy 2270 keV. The target thickness was chosen so as to stop all the beta particles of energy up to 546 keV. The beta particles from 90Y couldn’t be stopped by target and does not produce the bremsstrahlung. The geometrical arrangement for the present measurements of total bremsstrahlung spectral photon distributions in different thick target of lead compounds is shown in Fig. 1. A Cryo cool Si (Li) detector having resolution 155 eV at 5.9 keV is used for the present measurements. A Perspex beta stopper technique was employed to eliminate the contribution of internal bremsstrahlung (IB), bremsstrahlung generated in the source material and room background. Targets of Pb (CH3COO)2·3H2O (198 mg/cm2), Pb(NO3)2 (210 mg/cm2) and PbCl2 (209 mg/cm2) were used in the present measurements. The spectrometer was calibrated with standard gamma sources, and then two sets of measurements were taken for a time interval of 150,000 s by placing the target at position A and position B (Fig. 1). This method of measurement at two positions eliminates the contributions of internal bremsstrahlung, bremsstrahlung generated in the source material, characteristics X-rays, if any, of the element and the room background. The difference of the two measurements at position A and B gives the
(4)
1+k
90
Here, P(W′e)dW′e is the beta spectrum of the beta emitter under study. In the present measurement beta spectrum is taken from Laslett et al. (1950). At lower photon energy in thick targets, photon absorption correction due to detector elements, air and beryllium window play a very important role and can’t be neglected. These corrections have been successfully applied by Singh (2016). Therefore, by applying these corrections the corrected Scor (k,Z mod) is given as
Scor (k,Z mod) = RS(k,Z mod)ξ(k)exp (+ μx 0)
(5)
Here, ‘μ’ is the mass attenuation coefficient for the given target compound taken from the tabulations given by Chantler et al. (2005) and ′x 0′ is the optimum thickness of the target which is given by
x 0 = (x−R 0)
(6)
Where, ‘x’ is the target thickness in terms of mg/cm , R 0 is the mean range of beta particles in target as mentioned by Evans (1955) and ξ(k) is the detector efficiency. Computer programmes were written in Fortran to calculate S(k,Z mod) . The bremsstrahlung differential cross section was evaluated by using the above mentioned theoretical models, then by using the 2
3
Applied Radiation and Isotopes 130 (2017) 1–6
S.J. Sharma et al.
Fig. 3. (a–c) Plot of number of photons of energy k per m0c2 per unit total photon yield versus photon energy keV (Errors are lying within the experimental points).
using the mass attenuation coefficients tabulated by Chantler et al. (2005). The electron backscattering factor R was also incorporated in the measured bremsstrahlung spectral photon distributions. The geometrical full-energy peak detector efficiency for the detector is determined by using the values of the intrinsic efficiency of the Si (Li) detector given by the manufacturer and photo-fraction values measured at different photon energies. The measured experimental bremsstrahlung spectral photon distributions were than divided by the
bremsstrahlung produced in target material. The experimental measured BS spectra for Pb (CH3COO)2·3H2O, Pb (NO3)2, PbCl2 thick targets are converted into a true spectrum by applying the corrections due to self absorption of BS in the target material and Perspex beta stopper, electron backscattering and geometrical efficiency. The bremsstrahlung spectra are converted into a common channel width of 1 keV. The correction of self absorption of BS photons in air, target thickness and the Perspex beta stopper are applied by 4
Applied Radiation and Isotopes 130 (2017) 1–6
S.J. Sharma et al.
geometrical full-energy peak detector efficiency and were reduced to the number of photons of energy k per unit m0c2. Further, the experimental bremsstrahlung spectra are reduced to number of photons of energy k per unit energy interval by dividing the corrected data by channel width (in mo c 2 units). Finally, the corrected true experimental bremsstrahlung spectral photon distributions were plotted against the photon energy k (Fig. 2).
FmodBH+PB theory that includes PB in the BS spectra, in the photon energy region 4–10 keV but large discrepancies have been observed in experiment and theory in the photon energy range 1–3 keV for all the compound targets. It shows that PB effect is strong in the low energy range (1–10 keV), the discrepancies in 1–3 keV photon energy range are expectedly due to the uncertainties in the attenuation coefficients, large interference between OB and PB in this energy region.
3. Errors
5. Conclusions
The errors due to the full energy detection efficiency of the detector, counting statistics, electron backscattering and attenuation of bremsstrahlung photons in the target materials contributes in the present measurement. The measurements were taken over for 150,000 s and dead time of the detector is less than 1% which improved the accuracy of data better than 1% in entire photon energy region of 1–10 keV. The photo-fraction values were uncertain by less than 2% which resulted into an overall error of less than 3% in the geometrical full-energy peak detector efficiency of the detector. The errors in the mass attenuation coefficients of target, beta stopper and air thickness are less than 1%, except near the edge regions as reported in Chantler et al. (2005). The errors in calculation of electron backscattering R were less than 1%. According to Markowicz and VanGriken (1984) the maximum error in the Zmod formula was under 1%. In the present measurement the overall errors were estimated to be less than 10% in the entire photon energy region of 1–10 keV.
From the comparison of experimental and theoretical results, it is seen that experimental results are more close to the theoretical models that include the contribution of polarization bremsstrahlung in the total bremsstrahlung spectra. It concludes that polarization bremsstrahlung plays vital role in the formation of total bremsstrahlung spectra in thick lead compound targets produced by 90Sr beta particles, particularly in the studied photon energy region of 1–10 keV, the significant positive deviations from FmodBH + PB theory in photon energy range 1–3 keV may be possibly due to large interference of PB and OB, large uncertainties in attenuation coefficient, multiple photons scattering and anisotropic absorbance properties of compounds. The PB contribution is dominant in case of higher Zmod compounds and decreases with the increase in photon energy. The suppression in PB contribution due to the presence of large weight fraction of low Z elements clearly shows that the elemental environment around the lead also plays a major role in the formation of BS spectra, in the studied photon energy region. The comprehensive total bremsstrahlung spectra studies in more number of compounds and with beta emitter having different end point energies are required to check the behavior of amorphous and crystalline solids, anisotropic absorbance properties of solids, crystal lattice type and type of bonding among the elements in the formation of total bremsstrahlung spectra in compounds to improve the existing bremsstrahlung theories.
4. Results and discussions The experimental results of BS spectra of Pb(CH3COO)2·3H2O, Pb (NO3)2, PbCl2 compounds have been compared with theoretical models elwert Corrected (non-relativistic) Bethe Heitler theory (EBH), modified Elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for OB and modified Elwert factor (relativistic) Bethe Heitler theory which includes PB (Fmod BH+PB) in SA, in the photon energy range 1–10 keV. The results for S(k,Zmod)/T (number of photons of energy k per m0c2 per unit total photon yield) from theories and experiment are given in plots Fig. 3(a–c). Table 1 gives the idea about the percentage contribution of PB into OB in lead acetate trihydrate, lead nitrate and lead chloride compounds targets in the photon energy range 1–10 keV. In case of Pb (CH3COO)2·3H2O, it is evident from Fig. 3(a) that the experimental data is in better agreement with the Fmod BH+PB theory in the energy region 4–10 keV, but significant deviation has been observed between 1 and 3 keV. The experimental data deviates from Fmod BH theory by 45–27% at 1 keV and 10 keV energies respectively. The PB contribution is found to decrease from 24% to 15% for 1–10 keV photon energy. In case of Lead Nitrate Pb (NO3)2 Fig. 3(b), it is clear that experimental data points are in agreement with Fmod BH+PB theory with deviation less than 10% in 4–10 keV but deviation of 11–15% has been observed in 1–3 keV region. The PB contribution decreases from 36% to 20% in the given range of photon energy. There is a large deviation of experimental data from Fmod BH and EBH theory in the given energy region. From the Fig. 3(c), it is observed that in case of lead Chloride (PbCl2) the experiment is in good agreement with the Fmod BH+PB theory within 10% from 4 to 10 keV but significant deviations (13–16%) are seen in the energy range 1–3 keV. The PB contribution decreases with the increase in photon energy i.e. 40–30% in the studied energy region. The experimental results differ from Fmod BH theory by deviation of 87–53% in the given energy range. It has been observed that there is a continuous decrease of PB contribution into OB in BS spectra with increase in photon energy. The significant deviation from Fmod BH+PB theory is observed in all the compounds in 1–3 keV photon energy regions. Further the suppression in PB contribution has been observed with the decrease in (Zmod) of compounds in the studied energy region. In brief, the experimental results are in better agreement with
Acknowledgement Author would like to acknowledge the “IKG Punjab Technical University, Kapurthala” for support in the present research work. References Amusia, M., Kuchiev, M., Korol, A., Solov’ev, A., 1985. Bremsstrahlung of relativistic particles and dynamic polarizability of target atom. Sov. Phys. JETP 61, 224–227. Avdonina, N.B., Pratt, R.H., 1999. Bremsstrahlung spectra from atoms and ions at low relativistic energies. J. Phys. B: At. Mol. Opt. Phys. 32, 4261–4276. Berger, M., Seltzer, S., 2000. U.S. National Aeronautics and Space Administration Report No. NASA-SP 3012 1964 Current tabulation on Web:Prog.ESTAR. 〈http://physics. nist.gov/PhysRefData/Star/Text/ESTAR.html〉. Bethe, H., Heitler, W., 1934. On the stopping of fast particles and on the creation of positive electrons. Proc. R. Soc. Lond. A 146, 83–112. Chantler, C.T., Olsen, K., Dragoset, R.A., Chang, J., Kishore, A.R., Kotochigova, S.A., Zucker, D.S., 2005. X-Ray Form Factor, Attenuation and Scattering Tables (Version 2. 1) National Institute of Standards and Technology, Gaithersburg, MD, (2008, June). [Online] Available: 〈http://Physics.nist.gov./ffast〉. Evans, R.D., 1955. The Atomic Nucleus. McGraw-Hill, New York. Laslett, J., Jensen, E., Paskin, A., 1950. First-forbidden spectra and the beta spectrum of 90 Sr-90Y. Phys. Rev. 79 (412-412). Manjunatha, H.C., Rudraswamy, B., 2007a. Studies on external bremsstrahlung in thick target compounds. Nucl. Instrum. Methods Phys. Res. A 572, 958–960. Manjunatha, H.C., Rudraswamy, B., 2007b. Numerical method for external bremsstrahlung cross sections in compounds. Radiat. Meas. 42, 251–255. Manjunatha, H.C., Rudraswamy, B., 2012. External bremsstrahlung spectra of the 90Sr source in some lead compounds measured using NaI detector. Radiat. Meas. 47, 100–104. Manjunatha, H.C., Suresh, K.C., Rudraswamy, B., 2010. External bremsstrahlung of 147Pm in PbCl2 and CdO. Nucl. Instrum. Methods Phys. Res. A 619, 326–329. Manjunatha, M.V., Umesh, T.K., 2015. Effective atomic number of some rare earth compounds determined by the study of external bremsstrahlung. J. Radiat. Res. Appl. Sci. 8, 428–432. Markowicz, A.A., VanGriken, R.E., 1984. Composition dependence of bremsstrahlung background in electron-probe X-ray microanalysis. Annu. Chem. 56, 2049–2051. Seltzer, S.D., Berger, M.J., 1986. Bremsstrahlung energy spectra from electrons with kinetic energy 1 keV to 10 GeV incident on screened nuclei and orbital electrons of
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region of 1–100 keV. Phys. Lett. A 379, 1127–1132. Singh, T., Kahlon, K.S., Dhaliwal, A.S., 2009. Total bremsstrahlung spectral photon distributions in metallic targets in the photon energy range of 5–10 keV by 204Tl beta particles. Nucl. Instrum. Methods Phys. Res. Sect. B. 267, 737–741. Singh, T., 2016. Effect of incident electron energy of beta emitter on the formation of bremsstrahlung spectra in the photon energy region of 1–5 keV. Nucl. Instrum. Methods Phys. Res. B 388, 9–14.
neutral atoms with Z = 1–100. At. Data Nucl. Data Tables 35, 345–418. Semaan, M., Quarles, C.A., 2001. A model for low-energy thick-target bremsstrahlung produced in a scanning electron microscope. X-Ray Spectrom. 30, 37–43. Shivaramu, 1990. Modified Kramer's law for bremsstrahlung produced by complete beta particle absorption in thick targets and compounds. J. Appl. Phys. 68, 1225–1228. Singh, A., Dhaliwal, A.S., 2015. Studies of polarization bremsstrahlung and ordinary bremsstrahlung from 89Sr beta particles in metallic targets in the photon energy
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Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Thick target total bremsstrahlung spectra of lead compounds in the photon energy region 1–10 keV by 90Sr beta particles
MARK
⁎
Suhansar Jit Sharmaa,b, Tajinder Singhc, , Doordarshi Singhd, Amrit Singhe, A.S. Dhaliwalf a
I.K. Gujral Punjab Technical University, Kapurthala, India Department of Physics, B.B.S.B Polytechnic College, Fatehgarh Sahib, Punjab, India c Department of Physics, Mata Gujri College, Fatehgarh Sahib, Punjab, India d Department of Mechanical Engineering, B.B.S.B Engineering College, Fatehgarh Sahib, Punjab, India e Department of Physics, Sri Guru Teg Bahadur Khalsa College, Anandpur Sahib, Punjab, India f Department of Physics, Sant Longowal Institute of Engineering & Technology, Longowal (Sangrur), Punjab, India b
H I G H L I G H T S bremsstrahlung spectra in thick targets of Pb compounds by Sr in energy range 1–10 keV. • Total results show better agreement with the model which includes polarization bremsstrahlung in stripped approximation 3–10 keV. • Experimental show positive deviation in the photon energy region of 1–3 keV. • Results • Suppression of polarization bremsstrahlung has been observed due to the presence of large fraction of low Z elements. 90
A R T I C L E I N F O
A B S T R A C T
Keywords: Polarization bremsstrahlung Ordinary bremsstrahlung Lead compounds Beta particles
Total bremsstrahlung spectral photon distribution generated in thick targets of lead compounds Pb (CH3COO)2·3H2O, Pb(NO3)2 and PbCl2 by 90Sr beta particles has been investigated theoretically and experimentally in the photon energy region 1–10 keV. The experimental results are compared with the theoretical models describing ordinary bremsstrahlung and the theoretical model which includes polarization bremsstrahlung into ordinary bremsstrahlung, in stripped approximation. It is observed that the experimental results show better agreement with the model which describes bremsstrahlung in stripped approximation in the energy range 3–10 keV. However, the results show positive deviation in the photon energy region of 1–3 keV. Further, it has been found that there is a continuous decrease of polarization bremsstrahlung contribution into ordinary bremsstrahlung in the formation of total bremsstrahlung spectra with increase in photon energy. The suppression of polarization bremsstrahlung has been observed due to the presence of large fraction of low Z elements in the compounds. The results clearly indicate that polarization bremsstrahlung plays an important role in the formation of total bremsstrahlung spectra in compounds in the studied energy region.
1. Introduction The formation of total bremsstrahlung spectra in compounds is required to be studied for mono-energetic and continuous beta particles. Total bremsstrahlung amplitude (BS) is the sum of ordinary bremsstrahlung (OB) and polarization bremsstrahlung (PB). Further, the domination of either of OB or the PB in building the BS spectra in thick targets of compounds of various elements at different photon energies can be described in terms of bremsstrahlung energy spectrum. OB is produced due to the scattering of the incident charged particles in the coulomb field of the static target nuclei, whereas the PB is produced due
⁎
to the dynamic response of an atom in the external field of the incident charged particle. Amusia et al. (1985) has described that PB can be added with OB in a stripped approximation (SA) for non-relativistic electron energies, in terms of Born approximation. An equivalent method for the BS spectra in the (SA) has been given by Avdonina and Pratt (1999), which is efficient for obtaining the BS spectra for photon energies greater than the ionization potential of the outer shell electrons of the target atom. In SA, the production of PB is described by the decrease of OB due to screening of outer shell electrons which is completely compensated by additional PB produced by the same outer shell electrons.
Corresponding author. E-mail address: [email protected] (T. Singh).
http://dx.doi.org/10.1016/j.apradiso.2017.09.010 Received 24 March 2017; Received in revised form 21 August 2017; Accepted 7 September 2017 Available online 09 September 2017 0969-8043/ © 2017 Elsevier Ltd. All rights reserved.
Applied Radiation and Isotopes 130 (2017) 1–6
S.J. Sharma et al.
The importance of PB in the formation of the BS spectra in thick metallic targets by continuous beta particles in the low energy photon region has already been reported (Singh, 2016; Singh et al., 2009; Singh and Dhaliwal, 2015). Bremsstrahlung spectral photon distribution studies are rare in compound targets as compared to the metallic thick targets. Manjunatha and Umesh (2015) studied the effective atomic number of some rare earth compounds with the study of bremsstrahlung. Manjunatha and Rudraswamy (2007a) also studied OB in thick compounds by 204Tl beta emitter in the photon energy greater than 100 keV. Manjunatha and Rudraswamy (2012) measured the OB spectra of compounds of lead using 90Sr beta emitter and NaI scintillation detector in the photon energy region of 200–2000 keV. Manjunatha and Rudraswamy (2007b) evaluated the OB cross sections in compounds using lagrange interpolation method and using data of elements given by Seltzer and Berger (1986). Manjunatha et al. (2010) has studied the OB spectra in PbCl2 and CdO compounds using continuous beta particles and NaI(Tl) detector in the photon energy range 20–180 keV. An extensive study of literature on bremsstrahlung reveals that no study has been carried out to check the contribution of PB into OB in compounds in the low energy region of 1–10 keV. As PB contribution decreases with the increase in photon energy and there is maximum interference of OB and PB at low photon energy, so it will be interesting to see the role of PB in the formation of BS spectra of compounds. The factors like multiple photon scattering, anisotropy, and absorption of photons in the targets also play an important role at low photon energy. This study will be helpful to ascertain the role of these factors in the total BS spectra of compounds. In the present study, thick targets of lead compounds Pb (CH3COO)2·3H2O, Pb(NO3)2, PbCl2 with modified atomic numbers (Zmod) 42.11,50.04 and 62.95 respectively have been used. The comparison of experimental results with the theoretical models elwert corrected (non-relativistic) Bethe Heitler theory (EBH), modified elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for OB and modified elwert factor (relativistic) Bethe Heitler theory (Fmod BH+PB) which includes PB will reveal the accuracy of these theoretical models in determining the BS spectra of thick targets of lead compounds in the energy range 1–10 keV. In the present work, the modified atomic number (Zmod) of metallic compounds has been calculated from the formula given by Markowicz and VanGriken (1984). l wiz2i Ai l wz ∑i Ai i i
50
10
2
∑i
(1)
Here, Wi, Zi, Ai are weight fraction, atomic weight and atomic number of ith element in the compound. Zmod by Markowicz is found to be more accurate than mean atomic number Zmean and it was found to be in better agreement with experimental results of Shivaramu (1990). In a thick target bremsstrahlung, the contribution of the processes such as electron scattering, excitation and ionization plays a vital role. For continuous Beta particles Bethe and Heitler (1934) gave an expression for the bremsstrahlung spectral distribution n(k,W′e,Z) in a sufficiently thick target to absorb an electron of energy W′e with N atoms per unit volume. Semaan and Quarles (2001) incorporated the correction for the self absorption of bremsstrahlung photons in the target and electron backscattering are required for n(k,W′e,Z), in case of low energy thick target bremsstrahlung. The expression for bremsstrahlung spectral photon distribution in thick target of compounds is given as W′e
n cor (k,W′e,Z) = RN
∫ 1+k
dσ(We,k,Z mod)/dk d We (−dWe/dx)
Pb(CH3COO)2.3H2O
45
10
No. Of Photons Of Energy k per unit m0c
Z mod =
Fig. 1. Experimental set up for measuring the bremsstrahlung photon spectral distribution using 90Sr source 1) source holder 2) beta source 3) Perspex sheet 4) position A of target 5) position B of target 6) Be window 7) detector collimation 8) Si(Li) chip 9) lead shielding 10) Pre amplifier 11) lead collimation 12) working axis.
Pb(NO3)2 PbCl2
40
10
35
10
30
10
25
10
20
10
15
10
10
10
5
10
0
10
0
2
4
6
8
10
Photon Energy keV Fig. 2. Plot of number of photons of energy k per m0c2 per unit total photon yield versus photon energy keV.
from the different theoretical models i.e. Elwert corrected (non-relativistic) Bethe Heitler theory (EBH), modified Elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for OB and modified Elwert factor (relativistic) Bethe Heitler theory which includes PB (Fmod BH +PB) in SA, −dWe/dx is the total energy loss per unit path length of an
(2)
Here, dσ(We,k,Z mod)/dk is the singly differential cross section taken 2
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Table 1 Percentage contribution of PB into OB in lead acetate trihydrate, lead nitrate and lead chloride compounds targets in the photon energy range 1–10 keV. Photon energy
No. of photons of energy k per unit m0c2 per unit total photon yield
Target: Lead Acetate Trihydrate
EBH
FmodBH
FmodBH+PB
EXPERIMENT
PERCENTAGE CONTRIBUTION OF PB into OB
1 2 3 4 5 6 8 10 Target lead nitrate 1 2 3 4 5 6 8 10 Target lead chloride 1 2 3 4 5 6 8 10
7.01E−01 1.68E−01 3.33E−04 1.76E−10 3.05E−20 4.48E−26 2.28E−30 3.60E−33
6.70E−01 1.69E−01 3.39E−04 1.80E−10 3.14E−20 4.63E−26 2.36E−30 3.45E−33
8.80E−01 2.17E−01 4.23E−04 2.19E−10 3.76E−20 5.56E−26 2.76E−30 3.97E−33
9.70E−01 2.45E−01 4.84E−04 2.28E−10 3.95E−20 5.89E−26 2.98E−30 4.36E−33
24 22 20 18 17 17 15 15
5.70E−01 1.35E−02 6.77E−08 5.66E−14 8.72E−22 6.07E−28 2.00E−33 2.91E−36
5.50E−01 1.38E−02 6.89E−08 5.69E−14 8.97E−22 6.28E−28 1.58E−33 3.08E−36
8.65E−01 2.14E−02 1.03E−07 8.39E−14 1.32E−21 9.10E−28 2.09E−33 3.84E−36
9.62E−01 2.43E−02 1.18E−07 8.90E−14 1.42E−21 9.78E−28 3.12E−33 4.22E−36
36 35 33 32 32 31 24 20
0.46 0.00085 3.78E−11 6.72E−17 8.05E−23 9.58E−28 1.25E−35 6.13E−39
0.52 0.00107 3.84E−11 6.89E−17 2.32E−22 9.85E−28 1.54E−35 6.42E−39
0.86 0.00172 6.19E−11 1.09E−16 3.65E−22 1.54E−27 2.38E−35 9.17E−39
0.97 0.00198 7.20E−11 1.13E−16 3.79E−22 1.60E−27 2.52E−35 9.81E−39
40 38 38 37 37 36 35 35
stopping power values and unfolded beta spectrum in the programme the results were obtained for S(k,Zmod). Now, by applying the above mentioned corrections the results were obtained for Scor (k,Z mod) . The total photon yields T were obtained for different targets from graphical integration of the BS spectra from the plots of Scor (k,Z mod) versus photon energy k between kmin and kmax. Comparison of experimentally measured bremsstrahlung spectra for different targets and the theoretical results obtained from Eq. (6), are made in terms of the number of photons of energy k per m 0 c 2 per unit total photon yield versus photon energy to make the results independent of source strength and to eradicate the errors in the experimental results.
electron in a target material, which includes radiative and collision loss, these values are taken from the tabulations given by Berger and Seltzer (2000). Electron backscattering factor ‘R’ is given by
R=
1 − η(We, Z mod) 1 − η(We, Z mod)
k2
(3)
W2e
Here, We = 0.4Wmax , Wmax is the end point energy of beta particles and η(We, Z mod) is the total backscattering factor. The BS spectral photon distribution in terms of number of photons of energy k per unit m 0 c2 per beta disintegration for continuous beta particle is given by S(k, Z mod) .
2. Experimental details
Wmax
S(k,Z mod) =
∫
ηcor (W′e,k,Z mod)P(W′e)dW′e
The continuous beta particles produced from the pure beta emitter Sr of source strength 5 μCi. 90Sr undergoes decay into 90Y emits beta particles with end point energy of 546 keV. Further, 90Y undergoes decays to 90Zr with emission of beta particles having end point energy 2270 keV. The target thickness was chosen so as to stop all the beta particles of energy up to 546 keV. The beta particles from 90Y couldn’t be stopped by target and does not produce the bremsstrahlung. The geometrical arrangement for the present measurements of total bremsstrahlung spectral photon distributions in different thick target of lead compounds is shown in Fig. 1. A Cryo cool Si (Li) detector having resolution 155 eV at 5.9 keV is used for the present measurements. A Perspex beta stopper technique was employed to eliminate the contribution of internal bremsstrahlung (IB), bremsstrahlung generated in the source material and room background. Targets of Pb (CH3COO)2·3H2O (198 mg/cm2), Pb(NO3)2 (210 mg/cm2) and PbCl2 (209 mg/cm2) were used in the present measurements. The spectrometer was calibrated with standard gamma sources, and then two sets of measurements were taken for a time interval of 150,000 s by placing the target at position A and position B (Fig. 1). This method of measurement at two positions eliminates the contributions of internal bremsstrahlung, bremsstrahlung generated in the source material, characteristics X-rays, if any, of the element and the room background. The difference of the two measurements at position A and B gives the
(4)
1+k
90
Here, P(W′e)dW′e is the beta spectrum of the beta emitter under study. In the present measurement beta spectrum is taken from Laslett et al. (1950). At lower photon energy in thick targets, photon absorption correction due to detector elements, air and beryllium window play a very important role and can’t be neglected. These corrections have been successfully applied by Singh (2016). Therefore, by applying these corrections the corrected Scor (k,Z mod) is given as
Scor (k,Z mod) = RS(k,Z mod)ξ(k)exp (+ μx 0)
(5)
Here, ‘μ’ is the mass attenuation coefficient for the given target compound taken from the tabulations given by Chantler et al. (2005) and ′x 0′ is the optimum thickness of the target which is given by
x 0 = (x−R 0)
(6)
Where, ‘x’ is the target thickness in terms of mg/cm , R 0 is the mean range of beta particles in target as mentioned by Evans (1955) and ξ(k) is the detector efficiency. Computer programmes were written in Fortran to calculate S(k,Z mod) . The bremsstrahlung differential cross section was evaluated by using the above mentioned theoretical models, then by using the 2
3
Applied Radiation and Isotopes 130 (2017) 1–6
S.J. Sharma et al.
Fig. 3. (a–c) Plot of number of photons of energy k per m0c2 per unit total photon yield versus photon energy keV (Errors are lying within the experimental points).
using the mass attenuation coefficients tabulated by Chantler et al. (2005). The electron backscattering factor R was also incorporated in the measured bremsstrahlung spectral photon distributions. The geometrical full-energy peak detector efficiency for the detector is determined by using the values of the intrinsic efficiency of the Si (Li) detector given by the manufacturer and photo-fraction values measured at different photon energies. The measured experimental bremsstrahlung spectral photon distributions were than divided by the
bremsstrahlung produced in target material. The experimental measured BS spectra for Pb (CH3COO)2·3H2O, Pb (NO3)2, PbCl2 thick targets are converted into a true spectrum by applying the corrections due to self absorption of BS in the target material and Perspex beta stopper, electron backscattering and geometrical efficiency. The bremsstrahlung spectra are converted into a common channel width of 1 keV. The correction of self absorption of BS photons in air, target thickness and the Perspex beta stopper are applied by 4
Applied Radiation and Isotopes 130 (2017) 1–6
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geometrical full-energy peak detector efficiency and were reduced to the number of photons of energy k per unit m0c2. Further, the experimental bremsstrahlung spectra are reduced to number of photons of energy k per unit energy interval by dividing the corrected data by channel width (in mo c 2 units). Finally, the corrected true experimental bremsstrahlung spectral photon distributions were plotted against the photon energy k (Fig. 2).
FmodBH+PB theory that includes PB in the BS spectra, in the photon energy region 4–10 keV but large discrepancies have been observed in experiment and theory in the photon energy range 1–3 keV for all the compound targets. It shows that PB effect is strong in the low energy range (1–10 keV), the discrepancies in 1–3 keV photon energy range are expectedly due to the uncertainties in the attenuation coefficients, large interference between OB and PB in this energy region.
3. Errors
5. Conclusions
The errors due to the full energy detection efficiency of the detector, counting statistics, electron backscattering and attenuation of bremsstrahlung photons in the target materials contributes in the present measurement. The measurements were taken over for 150,000 s and dead time of the detector is less than 1% which improved the accuracy of data better than 1% in entire photon energy region of 1–10 keV. The photo-fraction values were uncertain by less than 2% which resulted into an overall error of less than 3% in the geometrical full-energy peak detector efficiency of the detector. The errors in the mass attenuation coefficients of target, beta stopper and air thickness are less than 1%, except near the edge regions as reported in Chantler et al. (2005). The errors in calculation of electron backscattering R were less than 1%. According to Markowicz and VanGriken (1984) the maximum error in the Zmod formula was under 1%. In the present measurement the overall errors were estimated to be less than 10% in the entire photon energy region of 1–10 keV.
From the comparison of experimental and theoretical results, it is seen that experimental results are more close to the theoretical models that include the contribution of polarization bremsstrahlung in the total bremsstrahlung spectra. It concludes that polarization bremsstrahlung plays vital role in the formation of total bremsstrahlung spectra in thick lead compound targets produced by 90Sr beta particles, particularly in the studied photon energy region of 1–10 keV, the significant positive deviations from FmodBH + PB theory in photon energy range 1–3 keV may be possibly due to large interference of PB and OB, large uncertainties in attenuation coefficient, multiple photons scattering and anisotropic absorbance properties of compounds. The PB contribution is dominant in case of higher Zmod compounds and decreases with the increase in photon energy. The suppression in PB contribution due to the presence of large weight fraction of low Z elements clearly shows that the elemental environment around the lead also plays a major role in the formation of BS spectra, in the studied photon energy region. The comprehensive total bremsstrahlung spectra studies in more number of compounds and with beta emitter having different end point energies are required to check the behavior of amorphous and crystalline solids, anisotropic absorbance properties of solids, crystal lattice type and type of bonding among the elements in the formation of total bremsstrahlung spectra in compounds to improve the existing bremsstrahlung theories.
4. Results and discussions The experimental results of BS spectra of Pb(CH3COO)2·3H2O, Pb (NO3)2, PbCl2 compounds have been compared with theoretical models elwert Corrected (non-relativistic) Bethe Heitler theory (EBH), modified Elwert factor (relativistic) Bethe Heitler theory (Fmod BH) for OB and modified Elwert factor (relativistic) Bethe Heitler theory which includes PB (Fmod BH+PB) in SA, in the photon energy range 1–10 keV. The results for S(k,Zmod)/T (number of photons of energy k per m0c2 per unit total photon yield) from theories and experiment are given in plots Fig. 3(a–c). Table 1 gives the idea about the percentage contribution of PB into OB in lead acetate trihydrate, lead nitrate and lead chloride compounds targets in the photon energy range 1–10 keV. In case of Pb (CH3COO)2·3H2O, it is evident from Fig. 3(a) that the experimental data is in better agreement with the Fmod BH+PB theory in the energy region 4–10 keV, but significant deviation has been observed between 1 and 3 keV. The experimental data deviates from Fmod BH theory by 45–27% at 1 keV and 10 keV energies respectively. The PB contribution is found to decrease from 24% to 15% for 1–10 keV photon energy. In case of Lead Nitrate Pb (NO3)2 Fig. 3(b), it is clear that experimental data points are in agreement with Fmod BH+PB theory with deviation less than 10% in 4–10 keV but deviation of 11–15% has been observed in 1–3 keV region. The PB contribution decreases from 36% to 20% in the given range of photon energy. There is a large deviation of experimental data from Fmod BH and EBH theory in the given energy region. From the Fig. 3(c), it is observed that in case of lead Chloride (PbCl2) the experiment is in good agreement with the Fmod BH+PB theory within 10% from 4 to 10 keV but significant deviations (13–16%) are seen in the energy range 1–3 keV. The PB contribution decreases with the increase in photon energy i.e. 40–30% in the studied energy region. The experimental results differ from Fmod BH theory by deviation of 87–53% in the given energy range. It has been observed that there is a continuous decrease of PB contribution into OB in BS spectra with increase in photon energy. The significant deviation from Fmod BH+PB theory is observed in all the compounds in 1–3 keV photon energy regions. Further the suppression in PB contribution has been observed with the decrease in (Zmod) of compounds in the studied energy region. In brief, the experimental results are in better agreement with
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