- Email: [email protected]
Angular distributions of X-rays emitted following L3 ionization of Au atoms by electron impact
Radiation Physics and Chemistry 102 (2014) 40–43
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Angular distributions of X-rays emitted following L3 ionization of Au atoms by electron impact G. Sestric, S. Ferguson, I. Wright, S. Williams n Angelo State University, Department of Physics and Geosciences, San Angelo, TX 76909, USA
H I G H L I G H T S
Au Lα and Lβ X-rays emitted isotropically following electron impact. Angular distribution of Au Ll X-rays exhibits weak anisotropy. Data was corrected for absorption of the characteristic X-rays within the Au target.
art ic l e i nf o
a b s t r a c t
Article history: Received 1 January 2014 Accepted 14 April 2014 Available online 21 April 2014
The angular distributions of Au Lα, Lβ, and Ll X-rays at forward angles 01 r ϕ r251 emitted following 15 keV electron impact have been measured in order to investigate the degree of induced alignment of the L3 subshell vacancies. After corrections for absorption of the characteristic X-rays within the Au target, our results suggest that the angular distributions of the Lα and Lβ X-rays are essentially isotropic, as no anisotropy was observed in our data outside of experimental uncertainties. However, the results of our experiments suggest that the angular distribution of the Au Ll X-rays may be weakly anisotropic. & 2014 Elsevier Ltd. All rights reserved.
Keywords: X-rays Angular distributions Electron impact
1. Introduction It has been suggested that when an atomic inner-shell vacancy with total angular momentum j41/2 is created by interaction with either a charged particle or a photon, the vacancy will be aligned due to the magnetic sublevels of the ion having a nonstatistical population (Flügge et al., 1972; Oh and Pratt, 1974; Scofield, 1976). Evidence of this phenomenon can be observed through experiments measuring the degree of linear polarization of the resultant characteristic radiation emitted or through experiments related to the angular distribution of the Auger electrons or characteristic radiation emitted as the vacancy is filled. The theoretical work of Berezhko and Kabachnik (1977) suggests that the angular distribution of the characteristic radiation is described by the relationship: dI=dΩ ¼ ðI o =4π Þ½1 þ αA20 P 2 ð cos ϕÞ
ð1Þ
where Ω is the solid angle, Io is the intensity of the radiation emitted over the entire 4π sr solid angle, α is the decay parameter n
Corresponding author. Tel.: þ 1 325 942 2242. E-mail address: [email protected] (S. Williams).
http://dx.doi.org/10.1016/j.radphyschem.2014.04.024 0969-806X/& 2014 Elsevier Ltd. All rights reserved.
which depends on the initial and final states of the ionized atom and the total angular momentum (Pálinkás et al., 1979), A20 is the degree of induced alignment of the vacancy state, and P2(cos ϕ) is the second-order Lengendre polynomial. The results of experiments performed by Kahlon et al. (1991) and Demir et al. (2003) which involved the measurements of the angular distributions of Au L-shell X-rays emitted following photoionization suggested that the angular distributions of the Lα and Ll X-rays were strongly anisotropic. However, the results of recent experiments (Alrakabi et al., 2013) were in agreement with previous reports by Yamaoka et al. (2002, 2003) that suggested that the angular distributions were only weakly anisotropic, if at all. The primary goals of the experiments described in this report were to measure the angular distributions of Au L-shell X-rays emitted following L3 ionization after electron impact and to compare the results to the theory of Berezhko and Kabachnik (1977). There have been no previous studies known to the authors where the angular distributions of Au L-shell X-rays produced by electron impact have been measured, and only three reports known to the authors related to the measurements of the angular distributions of L-shell X-rays emitted following electron impact (Pálinkás et al., 1979; Aydinol et al., 1980; Küst and Mehlhorn, 2001).
G. Sestric et al. / Radiation Physics and Chemistry 102 (2014) 40–43
41
2. Experimental procedure 2.1. Description of experiments The data presented in this report were obtained using a Mini-X X-ray tube (Amptek Inc., USA) with a 1.93 70.19 mg/cm2-thick Au anode and a 23.5 mg/cm2-thick Be end-window. The Mini-X was mounted on a rotatable stage so that the Au anode was situated above the center of the circular stage. Experiments were performed using an accelerating voltage of 15.0 70.1 kV and an electron current of 8.0 70.1 μA for 600 live time seconds. The resultant radiation was measured using a Princeton Gamma-Tech Si(Li) detector with a known efficiency which was kept in a fixed position relative to the center of the rotatable stage during all experiments. The detector's efficiency was measured using calibrated radioisotope sources and was compared to a theoretical efficiency model based on absorption coefficients from the NIST XCOM database (http://www.nist.gov/pml/data/xcom, 2013). A more detailed description of the method used for efficiency measurement has been included in a previous report (Williams and Quarles, 2008). A Pb collimator with a 2.5 mm hole was placed in front of the detector window and the uncertainty in ϕ for all experiments is conservatively estimated to be 70.121. The signal from the preamplifier was sent through an Ortec 572A amplifier with a built-in pile-up rejector. A schematic of the experimental setup is shown in Fig. 1.
Fig. 2. Typical spectrum, with the Lα, Lβ, and Ll X-ray peaks at energies of 9.71, 11.44, and 8.49 keV, respectively.
and subtracting this value from the total number of photons detected in the region of the peaks. Fig. 2 is of a typical spectrum, with the Lα, Lβ, and Ll X-ray peaks at energies of 9.71, 11.44, and 8.49 keV, respectively. All data was corrected for absorption of characteristic X-rays within the target and the Be end-window by application of the term:
2.2. Description of data analysis
f ðk; ϕÞ ¼ exp½ðμAu x1 þ μBe x2 Þ= cos ϕ;
The net counts associated with the X-rays were determined with the aid of Amptek ADMCA software. The average net counting rates for the Au Lα, Lβ, and Ll X-rays were 169, 93, and 11 counts per second, respectively. Lα, Lβ, and Ll X-ray peak widths were 247, 321, and 234 eV (FWHM), respectively. One difficulty encountered in experiments involving the measurements of the angular distributions of X-rays emitted as the result of electron impact that is not encountered in similar photoionization experiments is the subtraction of the resultant bremsstrahlung background, which also is angularly dependent (Gonzales et al., 2011; Gonzales and Williams, 2013). Background radiation was subtracted by averaging the number of counts detected in the ten channels on either side of the Lα, Lβ, and Ll X-ray peaks, determining the average number of bremsstrahlung counts per channel, multiplying this number by the number of channels across which the Lα, Lβ, and Ll X-ray peaks are spread,
where μAu and μBe are the attenuation coefficients for photons with energy k for Au and Be, respectively, taken from the NIST XCOM database (http://www.nist.gov/pml/data/xcom/), and x1/ cosϕ and x2/cosϕ are the distances that the photon travels through the Au target and Be window, respectively. Given the incident energy of the electrons and the Au L-shell electron energies, it seems reasonable that the value of x1 can be approximated to be the thickness of the Au target, as the ionization cross section is greatest for interactions near the surface of the target and decreases dramatically once the electron loses energy via bremsstrahlung emission or other interactions. Furthermore, only a small percentage of the L-shell X-rays measured in our experiments were emitted as the result of fluorescence caused by bremsstrahlung. Results obtained using the Monte Carlo simulation, PENELOPE (Baró et al., 1995), suggest that the percent of Lα, Lβ, and Ll X-rays emitted as the result of fluorescence in our experiments were approximately 6.7%, 7.2%, and 6.8%, respectively.
ð2Þ
3. Experimental results
Fig. 1. Diagram of the experimental setup.
Fig. 3 shows plots of the ratios of the intensities of the Au Lα, Lβ, and Ll X-rays at angles ϕ to the intensities of the respective X-rays at ϕ ¼ 01. The data suggest that the Au Lα and Lβ X-rays are essentially emitted isotropically, as no anisotropy was observed in our data outside of experimental uncertainties. This is not altogether surprising when the values of the decay parameters, α, are considered. The value of α for the Lα1 and Lα2 X-rays, taken from Berezhko and Kabachnik (1977), are 0.10 and 0.40, respectively. We were unable to resolve the Lα1 and Lα2 X-rays using the Si(Li) detector, and used a weighted average value of α ¼0.054 for all calculations involving the Lα X-rays, using the respective intensities taken from a simulation produced by the Monte Carlo code, PENELOPE (Baró et al., 1995), as the weighting factor. The same was done when calculating the value of α for the Lβ X-rays, resulting in a weighted average value of 0.053. However, the value of α for the Ll X-rays is 0.50 (Berezhko and Kabachnik, 1977),
42
G. Sestric et al. / Radiation Physics and Chemistry 102 (2014) 40–43
Fig. 4. Ratios of the intensities of the Au Ll X-rays to the nearly-isotropic Lα X-rays at forward angles ranging from 01 to 251. The curved line is the ratio of the [1þ αA20P2(cosϕ)] terms for the Ll X-rays and the Lα X-rays (with A20 ¼ 0.70), scaled to fit the experimental data.
Fig. 3. Ratios of the intensities of the Au Lα (filled triangles, top), Lβ (open circles, middle), and Ll (filled squares, bottom) X-ray lines at angles ϕ to the intensities at ϕ¼ 01 for forward angles ranging from 01 to 251. The solid lines correspond to the average values.
which suggests that the anisotropy of the angular distribution of the Ll X-rays should be much stronger than for the Lα and Lβ X-rays. The third plot (bottom) suggests that the angular distribution of the Ll X-rays may be weakly anisotropic. The data shown in Fig. 3 is in agreement with the results of the aforementioned photoionization experiments performed by Yamaoka et al. (2002, 2003) and Alrakabi et al. (2013), which suggest that the Au Lα and Lβ X-rays are emitted isotropically, and that the Ll X-rays are only weakly anisotropic, if at all. The experimental error was calculated by combining statistical uncertainties with uncertainties for the terms calculated using Eq. (2) and bremsstrahlung background subtraction (estimated to be 3.0% for the Lα and Lβ X-rays and 5.0% for the Ll X-rays) in quadrature. The total uncertainties in the terms calculated using Eq. (2) were determined by using the uncertainties in the attenuation coefficients (estimated to be 1.5% based on the results of Glover et al., 2010) and the uncertainty in target thickness (stated by the manufacturer to be 70.19 mg/cm2) and following the general procedure described by Taylor (1996). The total estimated errors in the data shown in Fig. 3 are all between 3% and 5%. The ratios of the intensities of the Au Ll X-rays (α ¼0.50) to the nearly-isotropic Lα X-rays (α ¼0.054) at forward angles ranging
from 01 to 251 are shown in Fig. 4. The intensities of the X-rays have been corrected for detector efficiency at their respective energies. The curve shown in Fig. 4 represents the ratio of the [1þ αA20P2(cos ϕ)] terms for the Ll X-rays and the Lα X-rays, scaled to fit the experimental data. The fit suggests that the degree of induced alignment, A20, is approximately 0.7. The trend observed in the data, a slight increase in the intensity of the Au Ll X-rays as ϕ increases from 01, was also observed in photoionization experiments performed by Yamaoka et al. (2003) and Alrakabi et al. (2013), suggesting that the value of A20 is negative. The data, however, is in disagreement with reports by Kahlon et al. (1991) and Demir et al. (2003), in which the angular distribution of the Au Ll X-rays was observed to have anisotropy opposite that shown in Fig. 4, suggesting that the value of A20 is positive. As we are unaware of any previous experiments involving the measurements of the angular distribution of Au L-shell X-rays emitted following electron impact, we have no experimental values with which to directly compare our measured degree of induced alignment. However, previous experiments (Küst and Mehlhorn, 2001; Küst et al., 2003) suggest that the degree of induced alignment, while dependent on the energy of the incident photon or charged particle, is only weakly dependent on the particle type, if at all. Photoionization experiments performed by Yamaoka et al. (2003) involving incident photon energies of approximately 13 keV measured the value of A20 to be approximately 0.21 70.04. The degree of induced alignment was measured by comparing the ratios of the intensities of the Au Ll X-rays (α ¼0.50) to the Lα1 X-rays (α ¼0.10), rather than both of the Lα X-rays (α ¼0.054), which may at least partially (along with the difference in incident particle energies) explain the discrepancy in measured values of A20. However, the uncertainties in the data shown in Fig. 4 suggest that the degree of induced alignment, measured by fitting the data, likely has a considerable uncertainty, as well.
4. Conclusions We have measured the angular distributions of the Au L-shell X-rays emitted following L3 ionization by 15 keV electron impact at forward angles 01r ϕ r251. Our results suggest that the Au Lα and Lβ X-rays are essentially emitted isotropically, as no anisotropy was observed in our data outside of experimental uncertainties. The results also suggest that the Ll X-rays may have a weakly
G. Sestric et al. / Radiation Physics and Chemistry 102 (2014) 40–43
anisotropic angular distribution. Our findings were in agreement with the results of photoionization experiments performed by Alrakabi et al. (2013) and Yamaoka et al. (2002; 2003). However, the results of our experiments are contrary to reports by Kahlon et al. (1991) and Demir et al. (2003), which suggest that the angular distributions of both the Lα and Ll X-rays are anisotropic and, in the case of the Ll X-rays, have a much more pronounced anisotropy than was observed in our experiments. The data presented in this report has not been corrected to include the effects of Coster–Kronig transitions. The results of a previous study (Küst and Mehlhorn, 2001) related to the L3 ionization of Xe atoms by electron impact suggest that the effects of Coster–Kronig transitions (which suppress emitted X-ray anisotropy) are relatively small when the energies of the incident electrons are near ionization thresholds. Also, no corrections have been made to account for the effects of the angular deflections of incident electrons prior to ionization (which would also suppress emitted X-ray anisotropy) and the authors of this report are unaware of any studies of the effects. In the future, it would be interesting to study the importance of both of these effects (however minor they may be) on the anisotropic angular distributions of characteristic X-rays. Additionally, more precise experimental studies are still needed to determine the extent of the induced alignment of the vacancy states produced when atoms are ionized by photons, electrons, and heavy incident particles. While there have already been several studies performed measuring the angular distribution of X-rays emitted as the result of photoionization, the results have been inconsistent and contradictory. Furthermore, there have been relatively few experiments performed related to the measurements of the angular distributions of X-rays emitted following electron or heavy ion impact, and there is certainly a need for more contributions to the inadequate collection of data that currently exists.
Acknowledgements Financial support from an Angelo State University Research Enhancement grant is gratefully acknowledged. We also are grateful to C.A. Quarles and the Texas Christian University Department of Physics and Astronomy for the loan of the detector used in the experiments described in this report.
43
References Alrakabi, M., Kumar, S., Sharma, V., Singh, G., Mehta, D., 2013. Alignment of L3 subshell vacancy states in Au, Bi, Th and U following photoionisation and effect of external magnetic field. Eur. Phys. J. D 67, 99. Aydinol, M., Hippler, R., McGregor, I., Kleinpoppen, H., 1980. Angular distribution of X-radiation following electron bombardment of free atoms. J. Phys. B: At. Mol. Phys. 13, 989–998. Baró, J., Sempau, J., Fernández-Verea, J.M., Salvat, F., 1995. PENELOPE: an algorithm for Monte Carlo simulation of the penetration and energy loss of electrons and positrons in matter. Nucl. Instrum. Methods Phys. Res., Sect. B 100, 31–46. Berezhko, E., Kabachnik, N., 1977. Theoretical study of inner-shell alignment of atoms in electron impact ionisation: angular distribution and polarisation of X-rays and Auger electrons. J. Phys. B: At. Mol. Phys. 10, 2467. Demir, L., Sahin, M., Kurucu, Y., Karabulut, A., Sahin, Y., 2003. Angular dependence of Ll, Lα, Lβ and Lγ X-ray differential and fluorescence cross-sections for Er, Ta, W, Au, Hg and Tl. Radiat. Phys. Chem. 67, 605–612. Flügge, S., Mehlhorn, W., Schmidt, V., 1972. Angular distribution of Auger electrons following photoionization. Phys. Rev. Lett. 29, 7–9. Glover, J., Chantler, C., Barnea, Z., Rae, N., Tran, C., 2010. Measurement of the massattenuation coefficients of gold, derived quantities between 14 keV and 21 keV and determination of the bond lengths of gold. J. Phys. B: At. Mol. Phys. 43, 085001. Gonzales, D., Cavness, B., Williams, S., 2011. Angular distribution of thick-target bremsstrahlung produced by electrons with initial energies ranging from 10 to 20-keV incident on Ag. Phys. Rev. A: At. Mol. Opt. Phys. 84, 052726. Gonzales, D., Williams, S., 2013. Angular distribution of bremsstrahlung produced by 10-keV and 20-keV electrons incident on a thick Au target. In: AIP Conference Proceedings 1525, 114-117. 〈http://www.nist.gov/pml/data/xcom/〉2013. Kahlon, K.S., Singh, N., Mittal, R., Allawadhi, K.L., Sood, B.S., 1991. L3-subshell vacancy state alignment in photon-atom collisions. Phys. Rev. A: At. Mol. Opt. Phys. 44, 4379–4385. Küst, H., Mehlhorn, W., 2001. Alignment after L3 ionization of Xe atoms by electron impact near threshold. J. Phys. B: At. Mol. Phys. 34, 4155–4167. Küst, H., Kleiman, U., Mehlhorn, W., 2003. Alignment after Xe L3 photoionization by synchrotron radiation. J. Phys. B: At. Mol. Phys. 36, 2073–2082. Oh, S., Pratt, R., 1974. Dependence of atomic photoeffect on a bound-electron magnetic substate. Phys. Rev. A: At. Mol. Opt. Phys. 10, 1198–1203. Pálinkás, J., Schlenk, B., Valek, A., 1979. Experimental investigation of the angular distribution of characteristic x-radiation following electron impact ionization. J. Phys. B: At. Mol. Phys. 12, 3273–3279. Scofield, J.H., 1976. Angular dependence of fluorescent x-rays. Phys. Rev. A: At. Mol. Opt. Phys. 14, 1418–1420. Taylor, J., 1996. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, second ed. University Science Books, Sausalito. Williams, S., Quarles, C.A., 2008. Absolute bremsstrahlung yields at 1351 from 53keV electrons on gold film targets. Phys. Rev. A: At. Mol. Opt. Phys. 78, 062704. Yamaoka, H., Oura, M., Takahiro, K., Takeshima, N., Kawatsura, K., Mizumaki, M., Kleiman, U., Kabachnik, N., Mukoyama, T., 2002. Angular distribution of Au and Pb L x rays following photoionization by synchrotron radiation. Phys. Rev. A: At. Mol. Opt. Phys. 65, 062713. Yamaoka, H., Oura, M., Takahiro, K., Morikawa, T., Ito, S., Mizumaki, M., Semenov, S., Cherepkov, N., Kabachnik, N., Mukoyama, T., 2003. Alignment following Au L3 photoionization by synchrotron radiation. J. Phys. B: At. Mol. Phys. 36, 3889–3897.
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Angular distributions of X-rays emitted following L3 ionization of Au atoms by electron impact G. Sestric, S. Ferguson, I. Wright, S. Williams n Angelo State University, Department of Physics and Geosciences, San Angelo, TX 76909, USA
H I G H L I G H T S
Au Lα and Lβ X-rays emitted isotropically following electron impact. Angular distribution of Au Ll X-rays exhibits weak anisotropy. Data was corrected for absorption of the characteristic X-rays within the Au target.
art ic l e i nf o
a b s t r a c t
Article history: Received 1 January 2014 Accepted 14 April 2014 Available online 21 April 2014
The angular distributions of Au Lα, Lβ, and Ll X-rays at forward angles 01 r ϕ r251 emitted following 15 keV electron impact have been measured in order to investigate the degree of induced alignment of the L3 subshell vacancies. After corrections for absorption of the characteristic X-rays within the Au target, our results suggest that the angular distributions of the Lα and Lβ X-rays are essentially isotropic, as no anisotropy was observed in our data outside of experimental uncertainties. However, the results of our experiments suggest that the angular distribution of the Au Ll X-rays may be weakly anisotropic. & 2014 Elsevier Ltd. All rights reserved.
Keywords: X-rays Angular distributions Electron impact
1. Introduction It has been suggested that when an atomic inner-shell vacancy with total angular momentum j41/2 is created by interaction with either a charged particle or a photon, the vacancy will be aligned due to the magnetic sublevels of the ion having a nonstatistical population (Flügge et al., 1972; Oh and Pratt, 1974; Scofield, 1976). Evidence of this phenomenon can be observed through experiments measuring the degree of linear polarization of the resultant characteristic radiation emitted or through experiments related to the angular distribution of the Auger electrons or characteristic radiation emitted as the vacancy is filled. The theoretical work of Berezhko and Kabachnik (1977) suggests that the angular distribution of the characteristic radiation is described by the relationship: dI=dΩ ¼ ðI o =4π Þ½1 þ αA20 P 2 ð cos ϕÞ
ð1Þ
where Ω is the solid angle, Io is the intensity of the radiation emitted over the entire 4π sr solid angle, α is the decay parameter n
Corresponding author. Tel.: þ 1 325 942 2242. E-mail address: [email protected] (S. Williams).
http://dx.doi.org/10.1016/j.radphyschem.2014.04.024 0969-806X/& 2014 Elsevier Ltd. All rights reserved.
which depends on the initial and final states of the ionized atom and the total angular momentum (Pálinkás et al., 1979), A20 is the degree of induced alignment of the vacancy state, and P2(cos ϕ) is the second-order Lengendre polynomial. The results of experiments performed by Kahlon et al. (1991) and Demir et al. (2003) which involved the measurements of the angular distributions of Au L-shell X-rays emitted following photoionization suggested that the angular distributions of the Lα and Ll X-rays were strongly anisotropic. However, the results of recent experiments (Alrakabi et al., 2013) were in agreement with previous reports by Yamaoka et al. (2002, 2003) that suggested that the angular distributions were only weakly anisotropic, if at all. The primary goals of the experiments described in this report were to measure the angular distributions of Au L-shell X-rays emitted following L3 ionization after electron impact and to compare the results to the theory of Berezhko and Kabachnik (1977). There have been no previous studies known to the authors where the angular distributions of Au L-shell X-rays produced by electron impact have been measured, and only three reports known to the authors related to the measurements of the angular distributions of L-shell X-rays emitted following electron impact (Pálinkás et al., 1979; Aydinol et al., 1980; Küst and Mehlhorn, 2001).
G. Sestric et al. / Radiation Physics and Chemistry 102 (2014) 40–43
41
2. Experimental procedure 2.1. Description of experiments The data presented in this report were obtained using a Mini-X X-ray tube (Amptek Inc., USA) with a 1.93 70.19 mg/cm2-thick Au anode and a 23.5 mg/cm2-thick Be end-window. The Mini-X was mounted on a rotatable stage so that the Au anode was situated above the center of the circular stage. Experiments were performed using an accelerating voltage of 15.0 70.1 kV and an electron current of 8.0 70.1 μA for 600 live time seconds. The resultant radiation was measured using a Princeton Gamma-Tech Si(Li) detector with a known efficiency which was kept in a fixed position relative to the center of the rotatable stage during all experiments. The detector's efficiency was measured using calibrated radioisotope sources and was compared to a theoretical efficiency model based on absorption coefficients from the NIST XCOM database (http://www.nist.gov/pml/data/xcom, 2013). A more detailed description of the method used for efficiency measurement has been included in a previous report (Williams and Quarles, 2008). A Pb collimator with a 2.5 mm hole was placed in front of the detector window and the uncertainty in ϕ for all experiments is conservatively estimated to be 70.121. The signal from the preamplifier was sent through an Ortec 572A amplifier with a built-in pile-up rejector. A schematic of the experimental setup is shown in Fig. 1.
Fig. 2. Typical spectrum, with the Lα, Lβ, and Ll X-ray peaks at energies of 9.71, 11.44, and 8.49 keV, respectively.
and subtracting this value from the total number of photons detected in the region of the peaks. Fig. 2 is of a typical spectrum, with the Lα, Lβ, and Ll X-ray peaks at energies of 9.71, 11.44, and 8.49 keV, respectively. All data was corrected for absorption of characteristic X-rays within the target and the Be end-window by application of the term:
2.2. Description of data analysis
f ðk; ϕÞ ¼ exp½ðμAu x1 þ μBe x2 Þ= cos ϕ;
The net counts associated with the X-rays were determined with the aid of Amptek ADMCA software. The average net counting rates for the Au Lα, Lβ, and Ll X-rays were 169, 93, and 11 counts per second, respectively. Lα, Lβ, and Ll X-ray peak widths were 247, 321, and 234 eV (FWHM), respectively. One difficulty encountered in experiments involving the measurements of the angular distributions of X-rays emitted as the result of electron impact that is not encountered in similar photoionization experiments is the subtraction of the resultant bremsstrahlung background, which also is angularly dependent (Gonzales et al., 2011; Gonzales and Williams, 2013). Background radiation was subtracted by averaging the number of counts detected in the ten channels on either side of the Lα, Lβ, and Ll X-ray peaks, determining the average number of bremsstrahlung counts per channel, multiplying this number by the number of channels across which the Lα, Lβ, and Ll X-ray peaks are spread,
where μAu and μBe are the attenuation coefficients for photons with energy k for Au and Be, respectively, taken from the NIST XCOM database (http://www.nist.gov/pml/data/xcom/), and x1/ cosϕ and x2/cosϕ are the distances that the photon travels through the Au target and Be window, respectively. Given the incident energy of the electrons and the Au L-shell electron energies, it seems reasonable that the value of x1 can be approximated to be the thickness of the Au target, as the ionization cross section is greatest for interactions near the surface of the target and decreases dramatically once the electron loses energy via bremsstrahlung emission or other interactions. Furthermore, only a small percentage of the L-shell X-rays measured in our experiments were emitted as the result of fluorescence caused by bremsstrahlung. Results obtained using the Monte Carlo simulation, PENELOPE (Baró et al., 1995), suggest that the percent of Lα, Lβ, and Ll X-rays emitted as the result of fluorescence in our experiments were approximately 6.7%, 7.2%, and 6.8%, respectively.
ð2Þ
3. Experimental results
Fig. 1. Diagram of the experimental setup.
Fig. 3 shows plots of the ratios of the intensities of the Au Lα, Lβ, and Ll X-rays at angles ϕ to the intensities of the respective X-rays at ϕ ¼ 01. The data suggest that the Au Lα and Lβ X-rays are essentially emitted isotropically, as no anisotropy was observed in our data outside of experimental uncertainties. This is not altogether surprising when the values of the decay parameters, α, are considered. The value of α for the Lα1 and Lα2 X-rays, taken from Berezhko and Kabachnik (1977), are 0.10 and 0.40, respectively. We were unable to resolve the Lα1 and Lα2 X-rays using the Si(Li) detector, and used a weighted average value of α ¼0.054 for all calculations involving the Lα X-rays, using the respective intensities taken from a simulation produced by the Monte Carlo code, PENELOPE (Baró et al., 1995), as the weighting factor. The same was done when calculating the value of α for the Lβ X-rays, resulting in a weighted average value of 0.053. However, the value of α for the Ll X-rays is 0.50 (Berezhko and Kabachnik, 1977),
42
G. Sestric et al. / Radiation Physics and Chemistry 102 (2014) 40–43
Fig. 4. Ratios of the intensities of the Au Ll X-rays to the nearly-isotropic Lα X-rays at forward angles ranging from 01 to 251. The curved line is the ratio of the [1þ αA20P2(cosϕ)] terms for the Ll X-rays and the Lα X-rays (with A20 ¼ 0.70), scaled to fit the experimental data.
Fig. 3. Ratios of the intensities of the Au Lα (filled triangles, top), Lβ (open circles, middle), and Ll (filled squares, bottom) X-ray lines at angles ϕ to the intensities at ϕ¼ 01 for forward angles ranging from 01 to 251. The solid lines correspond to the average values.
which suggests that the anisotropy of the angular distribution of the Ll X-rays should be much stronger than for the Lα and Lβ X-rays. The third plot (bottom) suggests that the angular distribution of the Ll X-rays may be weakly anisotropic. The data shown in Fig. 3 is in agreement with the results of the aforementioned photoionization experiments performed by Yamaoka et al. (2002, 2003) and Alrakabi et al. (2013), which suggest that the Au Lα and Lβ X-rays are emitted isotropically, and that the Ll X-rays are only weakly anisotropic, if at all. The experimental error was calculated by combining statistical uncertainties with uncertainties for the terms calculated using Eq. (2) and bremsstrahlung background subtraction (estimated to be 3.0% for the Lα and Lβ X-rays and 5.0% for the Ll X-rays) in quadrature. The total uncertainties in the terms calculated using Eq. (2) were determined by using the uncertainties in the attenuation coefficients (estimated to be 1.5% based on the results of Glover et al., 2010) and the uncertainty in target thickness (stated by the manufacturer to be 70.19 mg/cm2) and following the general procedure described by Taylor (1996). The total estimated errors in the data shown in Fig. 3 are all between 3% and 5%. The ratios of the intensities of the Au Ll X-rays (α ¼0.50) to the nearly-isotropic Lα X-rays (α ¼0.054) at forward angles ranging
from 01 to 251 are shown in Fig. 4. The intensities of the X-rays have been corrected for detector efficiency at their respective energies. The curve shown in Fig. 4 represents the ratio of the [1þ αA20P2(cos ϕ)] terms for the Ll X-rays and the Lα X-rays, scaled to fit the experimental data. The fit suggests that the degree of induced alignment, A20, is approximately 0.7. The trend observed in the data, a slight increase in the intensity of the Au Ll X-rays as ϕ increases from 01, was also observed in photoionization experiments performed by Yamaoka et al. (2003) and Alrakabi et al. (2013), suggesting that the value of A20 is negative. The data, however, is in disagreement with reports by Kahlon et al. (1991) and Demir et al. (2003), in which the angular distribution of the Au Ll X-rays was observed to have anisotropy opposite that shown in Fig. 4, suggesting that the value of A20 is positive. As we are unaware of any previous experiments involving the measurements of the angular distribution of Au L-shell X-rays emitted following electron impact, we have no experimental values with which to directly compare our measured degree of induced alignment. However, previous experiments (Küst and Mehlhorn, 2001; Küst et al., 2003) suggest that the degree of induced alignment, while dependent on the energy of the incident photon or charged particle, is only weakly dependent on the particle type, if at all. Photoionization experiments performed by Yamaoka et al. (2003) involving incident photon energies of approximately 13 keV measured the value of A20 to be approximately 0.21 70.04. The degree of induced alignment was measured by comparing the ratios of the intensities of the Au Ll X-rays (α ¼0.50) to the Lα1 X-rays (α ¼0.10), rather than both of the Lα X-rays (α ¼0.054), which may at least partially (along with the difference in incident particle energies) explain the discrepancy in measured values of A20. However, the uncertainties in the data shown in Fig. 4 suggest that the degree of induced alignment, measured by fitting the data, likely has a considerable uncertainty, as well.
4. Conclusions We have measured the angular distributions of the Au L-shell X-rays emitted following L3 ionization by 15 keV electron impact at forward angles 01r ϕ r251. Our results suggest that the Au Lα and Lβ X-rays are essentially emitted isotropically, as no anisotropy was observed in our data outside of experimental uncertainties. The results also suggest that the Ll X-rays may have a weakly
G. Sestric et al. / Radiation Physics and Chemistry 102 (2014) 40–43
anisotropic angular distribution. Our findings were in agreement with the results of photoionization experiments performed by Alrakabi et al. (2013) and Yamaoka et al. (2002; 2003). However, the results of our experiments are contrary to reports by Kahlon et al. (1991) and Demir et al. (2003), which suggest that the angular distributions of both the Lα and Ll X-rays are anisotropic and, in the case of the Ll X-rays, have a much more pronounced anisotropy than was observed in our experiments. The data presented in this report has not been corrected to include the effects of Coster–Kronig transitions. The results of a previous study (Küst and Mehlhorn, 2001) related to the L3 ionization of Xe atoms by electron impact suggest that the effects of Coster–Kronig transitions (which suppress emitted X-ray anisotropy) are relatively small when the energies of the incident electrons are near ionization thresholds. Also, no corrections have been made to account for the effects of the angular deflections of incident electrons prior to ionization (which would also suppress emitted X-ray anisotropy) and the authors of this report are unaware of any studies of the effects. In the future, it would be interesting to study the importance of both of these effects (however minor they may be) on the anisotropic angular distributions of characteristic X-rays. Additionally, more precise experimental studies are still needed to determine the extent of the induced alignment of the vacancy states produced when atoms are ionized by photons, electrons, and heavy incident particles. While there have already been several studies performed measuring the angular distribution of X-rays emitted as the result of photoionization, the results have been inconsistent and contradictory. Furthermore, there have been relatively few experiments performed related to the measurements of the angular distributions of X-rays emitted following electron or heavy ion impact, and there is certainly a need for more contributions to the inadequate collection of data that currently exists.
Acknowledgements Financial support from an Angelo State University Research Enhancement grant is gratefully acknowledged. We also are grateful to C.A. Quarles and the Texas Christian University Department of Physics and Astronomy for the loan of the detector used in the experiments described in this report.
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