Studies of total bremsstrahlung spectra in the oxides of lanthanides

Radiation Physics and Chemistry 141 (2017) 207–212

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Studies of total bremsstrahlung spectra in the oxides of lanthanides a,⁎

b

Amrit Singh , Tajinder Singh , A.S. Dhaliwal a b c

MARK

c

Baba Ajay Singh Khalsa College, Gurdas Nangal, Gurdaspur, Punjab, India Mata Gujri College, Fatehgarh Sahib, Punjab, India Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur, Punjab, India

A R T I C L E I N F O

A B S T R A C T

Keywords: Polarization bremsstrahlung Ordinary bremsstrahlung Lanthanide oxides Compounds

Total bremsstrahlung spectral photon distribution generated in thick targets of oxides of lanthanides (Pr6O11, Gd2O3, Tb4O7 and Er2O3) by 89Sr beta particles has been investigated in the photon energy region 1–100 keV. The experimental results are compared with the theory describing ordinary bremsstrahlung and the theory which includes polarization bremsstrahlung into ordinary bremsstrahlung in stripped approximation. It has been found that contribution of polarization bremsstrahlung into total bremsstrahlung in a target is limited to a low energy region only and also varies with the effective atomic number (Zeff) of target material. Further, it has been found that the suppression of polarization bremsstrahlung has been observed due to the presence of large fraction of low Z element oxygen in the compounds.

1. Introduction Total bremsstrahlung (BS) in a target, while interacting with a charged particle is the sum of the ordinary bremsstrahlung (OB) and polarization bremsstrahlung (PB). OB is produced due to interaction of charged particle with the static field of the target atom while, PB is produced due to dynamic response of target atom. Bethe and Heitler (1934) gave the basic theory for relativistic OB by using Born approximation and later this theory was corrected by Elwert (1939) for non-relativistic case. Further, by using the self consistent field wave functions Tseng and Pratt (1971) gave a theory for OB. General reviews on the theory of OB were given by Koch and Motz (1959), Seltzer and Berger (1985) and Pratt et al. (1995). The process of total bremsstrahlung (BS) was explained by Amusia (1988) in which the contribution of PB included into OB, for high but non-relativistic electron energies in a stripped (SA) approximation, with Born approximation. SA approximation approach neglects the specific structure of the bremsstrahlung cross section near each sub shell threshold, where polarization bremsstrahlung frequently becomes large in comparison with OB. Later Avdonina and Pratt (1999) gave the equivalent methods for the bremsstrahlung spectra, by using the stripped atom approximation and having contributions of PB into OB. They explained the bremsstrahlung spectra over an extensive range of photon energies and indicated that the contribution of PB decreases with increase in photon energy in the same way as the screening contribution to OB. Further, for relativistic electron energies, in the soft photon energy region of bremsstrahlung spectra, they explained that

⁎

Corresponding author. E-mail address: [email protected] (A. Singh).

http://dx.doi.org/10.1016/j.radphyschem.2017.07.017 Received 16 February 2017; Received in revised form 7 June 2017; Accepted 17 July 2017 Available online 18 July 2017 0969-806X/ © 2017 Elsevier Ltd. All rights reserved.

the contribution of PB is larger than in the non relativistic case and as photon energy increases, PB effect will decrease to zero. In the case of OB numbers of studies are available in the thick target of pure elements (Babu et al., 1975; Gopala et al., 1987; Dance et al., 1968; Ambrose et al., 1991; Gonzales et al., 2011). While in the case of PB only few studies (Williams and Quarles, 2008; Singh et al., 2008) are available in thick target of pure elements. Singh and Dhaliwal (2015, 2016) made studies for BS in thick targets and conclude that PB contributes in low energy and its production in the low-energy region due to the dynamic response of the target atom, suppresses the production of bremsstrahlung at higher energies. Most of the work was made by using metal thick targets, while measurements with compound thick targets are lacking. Only few studies are available with compound thick targets. Manjunatha and Rudraswamy (2011, 2012) and Manjunatha (2014) made few OB studies with 90Sr, 147Pm and 204Tl beta emitters in compounds of Lead and CdO with NaI(Tl) scintillation detector. In this paper, the studies of BS spectra in the thick target of oxides of lanthanide i.e., praseodymium oxide (Pr6O11), gadolinium oxide (Gd2O3), terbium oxide (Tb4O7) and erbium oxide (Er2O3) in the photon energy region of 1–100 keV for 89Sr (End point Energy= 1464 keV) beta particles are carried out. 89Sr beta emitter has an application in the treatment of osseous (bony) metastases preferentially in metabolically active section of the bone (Glenn et al., 2005; Mertens et al., 1998). The oxides of lanthanides have wide range of applications in the field of MRI, Light detection and ranging, remote sensing, as coloring agent in shielding glasses and goggles and in modern electronic systems. Hence, these measurements may facilitate to understand

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Fig. 1. Experimental setup for bremsstrahlung spectrum measurement. 1: Source holder. 2: Perspex Beta stopper (665 mg/cm2 Thick), 3: Perspex stand for source, 4: Perspex stand for holding beta stopper and target, 5: Lead Shielding (30 mm Thick), 6: Collimator (Diameter: 10.1 mm, Length: 10 mm), 7: Be Window (25 µm thick, active diameter 10 mm), (a) Distance between source and detector (18 mm), (b) Distance between source and target at position A (5 mm).

polarization bremsstrahlung into the total bremsstrahlung. Results reported earlier by Dhaliwal (2005) by using the similar technique of measurement are already authenticated by Czarnecki et al. (2016) through their measurements for mono-energetic along with the PENELOPE program. The present studies are required for indicating the importance of PB in the formation of BS spectra in compounds oven an energy region of 1–100 keV. The studies for compounds available in literature are above 100 keV of photon energy and that too for OB only. While understanding the process of bremsstrahlung, the variation and contribution of PB into OB in oxides of lanthanides is required to describe the BS in compounds. Further, it is also important to check the suppression bremsstrahlung production in the high photon energy regions due to the PB in the lower energy regions in the case of thick compound targets. It is expected that the present studies of PB and the OB in the oxides of lanthanides may contribute to understand the bremsstrahlung process, particularly for 89Sr beta source in the energy region of 1–100 keV. 2. Theory Fig. 2. Typical plots of number of counts versus photon energy (k) for a Pr6O11 target at position A and B for beta particles in the photon energy range of 1–100 keV.

Avdonina and Pratt (1999) gave an analytical expression for soft and hard photon energy region of the BS energy spectrum in terms of Gaunt factor, GBS (We, k , Z ) ,

the phenomena of PB and OB in lanthanides oxides over an energy region of 1–100 keV and shall describe their contributions in the lower and higher energy regions. These measurements are carried out with Si (Li) detector having high resolution and good efficiency in the energy region where the contribution of PB is dominant over OB. The experimentally measured BS spectra of thick targets of Pr6O11, Gd2O3, Tb4O7 and Er2O3 with 89Sr beta emitter are compared with the theoretical spectra obtained from the Elwert corrected non-relativistic Bethe Heitler theory (EBH), modified Elwert corrected relativistic Bethe Heitler theory (Fmod BH) without contribution of PB and theory of Avdonina and Pratt (Fmod BH +PB), which includes PB into OB. Results are compared in terms of number of photons of energy k per moc2 per unit photon yield. The Monte Carlo Simulations may not be useful here as the studies are carried out with a continuous beta particle. Moreover, the PENELOPE program is capable of simulating both bremsstrahlung and characteristic radiation emission. The code is based solely on ordinary bremsstrahlung theory given by Pratt et al. (1977). Later, Avdonina and Pratt (1999) incorporated the contributions of

GBS (We, k , Z ) = GB (We, k , Z ) −

q 3 ln ⎜⎛ + ⎟⎞ + GOB (We, k , Z ) π ⎝ q− ⎠

(1)

Here, the first term GB (We, k , Z ) is the bremsstrahlung energy spectrum for neutral atom in the Born approximation with screening parameter λo2 = 0.798Z , q ± = pi ± pf is the maximum and minimum momentum transfer, Z is the atomic number of the target material and GOB (We, k , Z ) is the modified corrected OB energy spectrum, given as,

GOB (We, k , Z ) = C (Ti , Z ) Fmod GBH (We, k , Z )

(2)

Here, C (Ti , Z ) is the higher order Born approximation factor which includes the multiple scattering effect to some extent, Fmod is the modified Elwert factor and GBH (We, k , Z ) is the Gaunt factor for the Bethe- Heitler cross-section. Bremsstrahlung in thick target depends on both the thin target bremsstrahlung cross-section and the electron energy loss and scattering in the target and the effect of secondary electron in the target. In 208

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Fig. 3. (a–d) Plots of number of BS photons of energy k per mo c 2 per unit photon yield versus photon energy k (keV) for Pr6O11, Gd2O3, Tb4O7 and Er2O3 compound targets for 89Sr beta particles in the photon energy region of 1–100 keV. Insets showing ratio of Experiment/Theory vs. Energy. (Errors are lying within the experimental points.).

Further, for continuous beta particles, the bremsstrahlung spectral photon distributions in an optimum thick target (minimum thickness required to stop the beta particle in target) for OB and BS are given by S (k , Zeff ) , i.e., the number of photons of energy k per unit mo c 2 per beta disintegration,

order to calculate the bremsstrahlung energy spectrum in thick targets of compounds expression given by Semaan and Quarles (2001) was used for incorporating the affects of electron backscattering factor (R) into the theoretical considerations. /

n (We/, k , Zeff ) = NR

we

∫1+k

dσ (We, k , Zeff )/ dk (−dWe / dx )

dWe

(3)

S (k , Zeff ) =

Here N is the number of atoms per unit volume to absorb a monoenergetic electron of energy We/ , − dWe / dx is the total energy loss per unit path length (collision stopping power and the radiation stopping power of the electrons). Zeff is the effective atomic number of the compound target. The values of Zeff for the compounds under study are taken from Singh et al. (2015). The term dσ (We, k , Zeff )/ dk is the singly differential bremsstrahlung cross-sections, this term is calculated separately for Elwert corrected (non relativistic) Bethe-Heitler [EBH] and modified Elwert factor (relativistic) Bethe-Heitler [Fmod BH] theories for OB and, Avdonina and Pratt [Fmod BH+PB] theory, which include the PB into OB in SA approximation. Values of total energy loss per unit path length of an electron are taken from the tabulations by Berger and Seltzer (2000).

Wmax

∫1+k

n (We/, k , Zeff ) P (We/) dWe/

(4)

Here P (We/) dWe/ is the beta spectrum of the 89Sr beta emitter under study and its values were obtained from the results reported by Langer and Price (1949). The theoretical bremsstrahlung spectra in terms of S (k , Zeff ) for Pr6O11, Gd2O3, Tb4O7, and Er2O3 targets for 89Sr beta emitter are obtained in the photon energy region of 1–100 keV from Eq. (4) for EBH and Fmod BH theories for OB and, Fmod BH+PB theory, for BS in SA approximation. For the present theoretical calculations the computer programs are written to calculate S (k , Zeff ) in FORTRAN for the different targets and theories of OB and PB. Moreover the various Monte Carlo calculations have been developed by using the ordinary bremsstrahlung cross sections given by Kissel et al. (1983) and Seltzer and 209

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Table 1 Theoretical and experimental values for bremsstrahlung spectra of Pr6O11 and Gd2O3 compound thick targets in the photon energy region of 1–100 keV. Photon Energy (keV)

Number of photons of energy k per moc2 per unit photon yield FmodBH Theory

EBH Target: Pr6O11 1 2 3 4 6 8 10 15 20 30 40 50 60 80 100 Target: Gd2O3 1 2 3 4 6 8 10 15 20 30 40 50 60 80 100

4.564 1.998 1.224 8.620 5.230 3.650 2.760 1.640 1.130 6.614 4.476 3.285 2.539 1.674 1.198

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04 10−04

5.270 2.307 1.413 9.951 6.037 4.217 3.184 1.898 1.307 7.636 5.168 3.793 2.932 1.932 1.384

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04 10−04

7.631 2.876 1.769 1.250 7.620 5.350 4.050 2.430 1.690 9.997 6.847 5.082 3.971 2.672 1.952

× × × × × × × × × × × × × × ×

FmodBH+PB Theory

10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04 10−04

1.089 3.842 2.265 1.550 9.030 6.120 4.510 2.570 1.710 9.549 6.245 4.462 3.373 2.147 1.497

8.810 3.321 2.043 1.443 8.798 6.172 4.678 2.811 1.949 1.154 7.905 5.868 4.585 3.085 2.254

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

1.258 4.436 2.615 1.790 1.042 7.064 5.208 2.969 1.978 1.103 7.210 5.151 3.894 2.479 1.728

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04 10−04

Experiment

1.160 3.960 2.290 1.580 9.680 6.500 4.410 2.560 1.820 1.090 7.487 5.208 4.221 3.172 2.411

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

1.340 4.576 2.646 1.826 1.119 7.511 5.096 2.958 2.103 1.260 8.768 6.019 4.878 3.666 2.786

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

a material, i.e., 657 mg/cm2. The contributions of internal bremsstrahlung (IB), bremsstrahlung generated in the source material, characteristics X-ray, if any, and room background are eliminated by employing Perspex beta stopper technique and placing the target at position A and B (Fig. 1). In the first measurement, at position A, the contribution of BS (target), IB, BS generated in the source material and room background, attenuated in the target and the Perspex beta stopper, having thickness more than the range of beta emitter are recorded. For the second measurement, the target placed at position B, so that the beta particle did not reach it. This measurement records the contribution of IB, BS generated in the source material, BS generated in the Perspex stopper and room background. The Perspex beta stopper and the target below it further attenuated these contributions. The contribution of BS produced in the first few layers of the Perspex beta stopper are very small as these contributions are attenuated by the rest of its thickness, which are further attenuated by the thick target below it. The difference of the above two measurements gives the information about the BS produced in target elements only. The remaining contribution of characteristics X-rays of the compound is removed by smoothing the spectrum under the peak and by using the extrapolation method. Typical measurements for a Pr6O11 target taken at positions A and B are shown in Fig. 2. The BS produced in the Perspex (Z = 4.6) is small and is also incorporated in the measurement. Measurements are taken for a time interval of 200,000 s for improvement in statistics of data better than 1% throughout the studies energy regions. The geometrical full energy peak detection efficiency of the Si(Li) detector is determined by taking the product of the photo-fraction values and the intrinsic efficiency of the detector at the particular photon energy. The corrections for the geometrical full-energy peak detector efficiency of the detector, Compton continuum and backscattering, i.e., response functions of Si(Li) detector, are applied to the measured spectra for Pr6O11, Gd2O3, Tb4O7 and Er2O3 target materials for their

Berger (1985) and no codes are available for total bremsstrahlung, i.e., OB+PB. Further, the theoretical distributions are converted into the number of photons of energy k per mo c 2 per unit photon yield for comparison with the experimental results by dividing them with the total photon yield (T) per beta disintegration. The values of T for different target materials are obtained from graphical integration of the BS spectra from the plots of S (k , Zeff ) versus photon energy k between kmin and kmax, i.e., 1 keV and 100 keV. This method makes results independent of source strength and eradicates the uncertainties in the experimental results. In this method the S (k , Zeff ) measures the number of photons of energy k per mo c 2 per beta disintegration and total photon yield (T) measures the total number of photons per beta disintegration. The ratio of these two quantities eliminates the effect of source strength in the measurements. Further, this method gives better accuracy over the normalization procedure. 3. Experimental details 89

Sr beta source of activity of ~ 5 mCi was used for the present measurements. CANBERRA made Cryo-cool Si(Li) detector, with active area of 80 mm2 and thickness 5 mm and having resolution of 155 eV at 5.9 keV was used for the bremsstrahlung spectrum measurements. The geometrical arrangement used for present measurement is shown in Fig. 1. The beta source is kept at a distance of 2.3 cm from a properly shielded Si(Li) detector to reduce the background counts to low level. The bremsstrahlung spectral photon distributions of Pr6O11, Gd2O3, Tb4O7 and Er2O3 compounds thick targets produced by 89Sr beta particles are measured by using Si(Li) detector in the photon energy region of 1–100 keV. The values of Zeff for these compounds taken from Singh et al. (2015) are 57.57, 62.93, 63.78 and 67.01, respectively. The thicknesses of the targets are in the range of the beta particles of 89Sr in 210

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Table 2 Theoretical and experimental values for bremsstrahlung spectra of Tb4O7 and Er2O3 compound thick targets in the photon energy region of 1–100 keV. Photon Energy (keV)

Number of photons of energy k per moc2 per unit photon yield FmodBH Theory

EBH Target: Tb4O7 1 2 3 4 6 8 10 15 20 30 40 50 60 80 100 Target: Er2O3 1 2 3 4 6 8 10 15 20 30 40 50 60 80 100

6.116 2.677 1.640 1.155 7.008 4.891 3.698 2.198 1.514 8.863 5.998 4.402 3.403 2.243 1.606

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04 10−04

5.975 2.615 1.602 1.128 6.845 4.782 3.611 2.152 1.482 8.658 5.860 4.301 3.324 2.191 1.569

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04 10−04

1.023 3.854 2.370 1.675 1.021 7.169 5.427 3.256 2.265 1.340 9.175 6.810 5.321 3.581 2.616

× × × × × × × × × × × × × × ×

FmodBH+PB Theory

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

1.460 5.148 3.035 2.077 1.210 8.210 6.043 3.444 2.291 1.280 8.368 5.979 4.520 2.877 2.006

9.990 3.765 2.316 1.636 9.975 6.998 5.304 3.187 2.210 1.309 8.963 6.653 5.198 3.498 2.556

× × × × × × × × × × × × × × ×

10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

1.426 5.030 2.965 2.029 1.182 8.010 5.905 3.366 2.243 1.250 8.175 8.841 4.416 2.811 1.960

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

Experiment

1.528 5.217 3.017 2.081 1.275 8.563 5.810 3.373 2.398 1.436 9.995 6.861 5.561 4.179 3.176

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

1.458 4.997 2.878 1.986 1.217 8.169 5.542 3.217 2.287 1.370 9.535 6.546 5.305 3.987 3.030

× × × × × × × × × × × × × × ×

10−01 10−02 10−02 10−02 10−02 10−03 10−03 10−03 10−03 10−03 10−04 10−04 10−04 10−04 10−04

10%. Beyond 22 keV, the experimental results are closer to Fmod BH theory. The variations of experimental results from Fmod BH theory are 7% at 30 keV, 10% at 60 keV and 23% at 100 keV photon energy. The decrease in the contributions of PB into BS is observed in the photon energy region of 1–22 keV. The contribution of PB reduces to 1% at 22 keV photon energy from 30% at 1 keV. From Fig. 3(c), it is observed that, the experimental results for Tb4O7 target are in agreement with Fmod BH+PB theory up to 22 keV within 10%. In the photon energy region above 22 keV the measured results are close to Fmod BH theory. The experimental results show the deviations of 7% at 35 keV to 22% at 100 keV photon energy from Fmod BH theory. Table 2, indicates that the PB contribution decreases from 30% at 1 keV to 1% at 22 keV. The experimental BS spectrum of Er2O3 target (Fig. 3(d)) is in agreement with Fmod BH+PB theory up to photon energy of 24 keV within 10% and above this it is closer to Fmod BH theory. The variations of experimental results from Fmod BH theory are found to be 8% at 40 keV and 20% at100 keV. It is clear from Table 2 that the PB contribution decreases with increase in photon energy, i.e. from 31% at 1 keV to 1% at 24 keV. The distributions obtained from EBH theory for OB are in complete disagreement with the experimental measurement of all compound targets over the entire energy range from 1 to 100 keV.

comparison with the theoretical distributions. Here the large values of photo-fraction and photoelectric absorption cross-section for low energy photons, the corrections due to Compton continuum, Silicon K Xray escape peak and Ar K X-ray peak, if any are found to be negligible. Finally, experimental bremsstrahlung spectra of all targets are converted into the number of photons of energy k per unit mo c 2 per unit of photon yield for comparison with the theoretical distributions obtained from EBH, and Fmod BH theories for OB and Fmod BH+PB for BS. The statistics of the data, measurement of geometrical full-energy peak detection efficiency of the detector and Compton Continuum are contributing to the overall errors in the measurements. These uncertainties are found to be less that 8% in the entire photon energy region of 1–100 keV. 4. Results and discussion The experimental results of BS spectra of Pr6O11, Gd2O3, Tb4O7 and Er2O3 compounds have been compared with theoretical measurements from EBH theory, Fmod BH theory for OB and Fmod BH+PB theory in SA in the photon energy range 1–100 keV. The results in terms of number of photons of energy k per m0c2 per unit total photon yield from theories and experiment measurements are shown in Fig. 3[a-d] and values are given in Tables 1 and 2. In case of Pr6O11 target, it is clear from Fig. 3(a) that the experimentally measured BS spectrum is in agreement with Fmod BH +PB theory up to photon energy of 21 keV within 10% and afterward experimental results are close to the Fmod BH theory. The deviation between the experimental results and the Fmod BH theory is 8% at 20 keV and 24% at 100 keV. Further, it is clear from Table 1 that PB contribution decreases from 29% at 1 keV to 1% at 21 keV photon energies. In the case of the Gd2O3 target (Fig. 3(b)), the experimental results are in agreement with the Fmod BH+PB theory from 1 keV to 22 keV within

5. Conclusions From the results, it is concluded that PB plays important role in the formation of BS spectra in thick compound targets produced by 89Sr beta particles, particularly in the low energy region. The PB contribution is dominant in case of higher Zeff compounds. The suppression in PB contribution due to the presence of the elemental environment around the lanthanides also plays a major role in the formation of BS spectra, in the studied energy region. Low Z elements oxygen present in 211

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the compounds suppresses the dominance of PB in BS spectra. Comprehensive BS spectra studies in different compounds and with beta emitter having different end point energies are required to ensure the behavior of amorphous and crystalline solids, anisotropic properties of solids, crystal lattice and role of type of bonding among the elements in the formation of 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 included in the theory to improve the accuracy of the theory. References Ambrose, R., Kahler, D.L., Lehtihet, H.E., Quarles, C.A., 1991. Nucl. Instrum. Methods B 57, 327–329. Amusia, M. Ya, 1988. Phys. Rep. 162, 249–335. Avdonina, N.B., Pratt, R.H., 1999. J. Phys. B: At. Mol. Opt. Phys. 32, 4261–4276. Babu, R.P., Murty, K.N., Murty, V.A.N., 1975. J. Phys. G 1, 273–285. 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. Proc. R. Soc. Lond. A 146, 83–112. Czarnecki, S., Short, A., Williams, S., 2016. Nucl. Instrum. Methods Phys. Res. B. 378, 54–58. Dance, W.E., Rester, D.H., Farmer, B.J., Johnson, J.H., 1968. J. Appl. Phys. 39,

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