ECPSSR Theory Research Articles

L-shell ionization of Cd, Sb, Te, Ba, La, Eu, Tb and Yb by 16O ions in the energy range from 0.19 to 0.75 MeV u−1

Lα1,2, Lβ1,3,4, Lβ2,15, Lγ1(5) and Lγ2,3(4,4′) X-ray production cross-sections have been measured on selected medium-Z elements using 16O ions with energies from 0.19 to 0.75 MeV u−1. Calculated L-subshell ionization cross-sections were compared with the predictions of the direct ionization theories: the ECPSSR theory, the semiclassical approximation (SCA) in the united atom limit (SCA-UA) and SCA coupled-channel calculations (SCA-CC) involving a few lowest lying states. For the ECPSSR theory, large discrepancies were found for all three subshells. Better overall agreement between the experiment and theory was found for the SCA-UA theory. SCA-CC calculations improved the agreement between experiment and theory for the L2-subshell in the very adiabatic region. By measuring the Lα X-ray production cross-sections on W targets of different thickness, possible contribution of electron capture (EC) to the X-ray production cross-section was estimated to be less than 20%. The degree of multiple ionization of outer shells caused by heavy ion bombardment was estimated from the X-ray line energy shifts and by comparing the X-ray intensity ratios for heavy ions and protons.

Deviations of the Kβ/Kα intensity ratio of Ti upon impact with low velocity ions

Deviations of the branching ratio of the decay of K-vacancies in Ti have been observed during bombardment with low velocity ions of H, He and N. Beams of these ions have been used for various applications in which resonant nuclear reactions were used as the main analytical technique, whereas the X-ray signal could conveniently be used for monitoring the accumulated charge. During the evaluation of this monitoring signal, it was observed that the commonly made assumption that the Kβ/Kα intensity ratio is a constant can easily be off by 30% or more. Also a few data of L-shell ionisation cross sections has been measured on Au to establish if the onset of deviations in the branching ratio parallels the onset of deviations from the ECPSSR theory for inner shell ionisation.

Charge state dependence of L-shell X-ray production cross sections of 28Ni, 29Cu, 30Zn, 31Ga and 32Ge by 12 MeV 16Oq+ ions

L-shell X-ray production cross sections of elements from Z2=28 to 32 were measured. A 12 MeV incident oxygen beam, with and without K-shell vacancies, was used to make a charge state dependence analysis. Simultaneous measurements were made of both scattered particles and X-rays from the ultra-clean foils that had been made sufficiently thin to reach the single-collision regime. Target L-shell to projectile K-shell electron capture for hydrogen-like (q=Z1−1) and fully stripped (q=Z1) oxygen ions were then extracted. The measurements are compared with the predictions of the ECPSSR theory using a single-hole fluorescence yield. In general and contrast to the first Born calculations, this theory gives reasonable agreement with the data for oxygen ions without K vacancies. However, the ECPSSR still significantly overpredicts the data for oxygen ions with K vacancies.

L-subshell ionization cross sections of some rare-earth elements by impact of 2 MeV ions: dependence on atomic number

Measurements of L-shell x-rays and Rutherford backscattering in some rare-earth elements produced by 2 MeV ions were used to study the dependence of individual L-subshell ionization cross sections on atomic number. The results were compared with the theoretical predictions of the ECPSSR theory. The discrepancies observed were reduced but not completely overcome by the inclusion of modifications to the theory, known as ECPSSR-IS and ECPSSR-IS-UA, which favour vacancy transfer from the -subshell to the - and -subshells. The theoretical models used for the comparison with experiment could successfully predict the functional dependence of -subshell ionization cross section on atomic number, but not the functional parameters.

L-subshell ionization cross-sections of Yb by impact of 1.0-8.5 MeV4He2+ ions

L-subshell ionization induced by 1.0–8.5 MeV 4He2+ was measured experimentally for a thin target of Yb using simultaneous acquisition of PIXE and RBS yields. The data were compared with the theoretical predictions of the ECPSSR theory and its extensions known as the ECPSSR-IS and ECPSSR-IS-UA theories. Good agreement was found for the L1- and L3-subshells at energies higher than about 5 MeV, whereas a fair agreement with the theory was observed for the L2-subshells. Possible reasons for the discrepancies are discussed in the framework of vacancy transfer from the L1- to the L2- and L3-subshells. © 1998 John Wiley & Sons, Ltd.

L X-ray production cross sections of medium Z elements by 4He ion impact

L X-ray production cross sections for 500, 600, 800 and 1000 keV 4He ions incident upon 47Ag, 49In, 50Sn, 51Sb, 52Te, and 58Ce targets are reported. Commercially available evaporated thin metal foils with thicknesses ranging between 45 and 160 μg/cm 2 were used. The experimental values of L X-ray production cross sections are compared to the predictions of the first Born and ECPSSR theories. The first Born approximation overpredicts the experimental values of all measured production cross sections for all elements and energies. ECPSSR theory underpredicts Lα, Lβ and L γ1,5 production cross sections for all elements except for Ce. Discrepancy is clearly larger at lower ion energies. On the other hand L γ2,3 is generally in good agreement with the ECPSSR theory. Only a very limited number of data for the same elements and energies as measured in this work are found in literature and compared with our values.

Measurements of ionization cross sections of Ti and Cu induced by low energy Li and B ion impact

The measurements of K-shell ionization cross sections of Ti and Cu induced by Li and B impact in the energy range of 1.0 MeV < E 0<6.4 MeV are presented. The correction of the fluorescence yield due to the multiple ionization is estimated. Extracted cross sections are compared to the predictions of different models: the ECPSSR theory and the SCA theory where quite a few approaches are used. The ECPSSR theory explains measured cross sections quite well. By including the correction of electron binding energy in the SCA theory in the same way as included in the ECPSSR theory the agreement between the measured and the SCA theoretical cross sections is improved.

L AND M X-RAY PRODUCTION CROSS SECTIONS OF HEAVY RARF EARTH ELEMENTS IN THE 3-40 MeV/amu PROJECTILE-ENERGY RANGE

Partial L- and M-x-ray production cross sections for Dy , Er and Lu have been systematically measured over the wide projectile-energy range of 3-40 MeV/amu for proton and 3 He -ion impact, and values of partial x-ray production cross sections were compared with those predicted by the ECPSSR theory. As the result, it is confirmed that the ECPSSR theory gives consistent ionization cross sections for each subshell in L- and M-shells. It is also found that values of x-ray transition rate are correct for Mα,β and Lα12 lines which are predominant in M and L x-ray spectra, respectively. However, it is pointed out that some of the values of x-ray transition rates must be revised, and improved values were obtained experimentally for the first time.

Ion-induced L x-ray emission cross sections of ytterbium

Measured L x-ray ionization cross sections for bombardment of Yb in the energy range 1.0 - 8.5 MeV are compared with the ECPSSR theory. Significant discrepancies between theory and experiment are observed at an incident beam energy below about 5 MeV. The discrepancies are greatly reduced by the inclusion of collision-induced intrashell coupling (ECPSSR-IS) and modifications of the binding factor in the theory in the united atom picture (ECPSSR-IS-UA). More specifically, in this case of Yb L-shell ionization by energetic ions, the contribution of L-subshell coupling towards better agreement with the theory is more significant than binding energy correction.

L x-ray production in lanthanide elements by 1 - 5 MeV helium ions

L x-ray production in and was measured for bombardment in the energy range 1 - 5 MeV. Very thin target foils were used, and x-ray yields were measured simultaneously with elastically scattered ions. The L-shell and individual and production cross sections and their ratios were extracted. These cross sections are compared to the results of the ECPSSR theory (energy-loss and Coulomb deflection effects, perturbed stationary state approximation with the relativistic correction), its united-atom (UA) extension UA-ECPSSR and the UA-ECPSSR-MI, which also accounts for multiple ionization (MI). With a few exceptions, the standard ECPSSR appears to be better than its modifications when and ratios are analysed. and and total L x-ray production cross sections, however, are in the best overall agreement with the UA-ECPSSR-MI theory.

Relative intensities and of Yb by impact of 1.0 - 8.5 MeV ions

The PIXE spectra resulting from ion beam bombardment in the energy range of 1.0 - 8.5 MeV of a thin target of ytterbium were measured to obtain the relative intensity and of L-shell lines. The results are compared with the calculated L-shell line intensities for helium ion impact in the ECPSSR theory. Modifications of the theory for intra-shell coupling were also calculated and compared with the measured intensities. Good agreement between experimental results and theoretical calculations was found for ion energies greater than 4 MeV. Possible reasons for the discrepancies observed at energies less than 4 MeV were discussed in the framework of the L-subshell coupling effect and binding energy corrections in the united-atom modifications of the ECPSSR theory.

M-shell x-ray production cross section measurements in Pb and Bi due to the impact of protons and nickel ions

M-shell x-ray production cross sections in Pb have been measured using 58 - 82 MeV ions and those in Bi by 1 - 5 MeV protons and 58 - 82 MeV ions (q = 5, 6). The experimental results have been compared with the predictions of the plane-wave Born approximation (PWBA) and with the calculations of the perturbed stationary state theory (ECPSSR) accounting for the energy loss (E), Coulomb deflection (C) and relativistic (R) effects. The present results of proton impact on bismuth have also been compared with the experimental data available from other investigations. To the best of our knowledge, the M-shell x-ray production cross sections in Pb and Bi by Ni-ion impact are reported here for the first time. Good agreement of the present results with the predictions of the ECPSSR theory has been observed for the total M x-ray cross sections in Bi due to proton impact while discrepancies to a factor of 1.5 - 2.5 in the case of total M x-ray cross sections have been observed between the present experimental and theoretical (PWBA and ECPSSR, respectively) results for Pb and Bi in the case of Ni-ion impact. These discrepancies between the experimental and theoretical results could be attributed to the effect of multiple ionization on the x-ray emission probabilities. If the modified value of the average fluorescence yield accounting for the outer-shell multiple ionization is used, the theoretical results of total M-shell x-ray cross sections based on the PWBA theory show fair agreement with the experimental results (within experimental uncertainties) while the ECPSSR theory is found to underestimate the experimental results by about 40% for both Pb and Bi in the case of Ni-ion impact. Furthermore, the and x-ray cross sections have been evaluated experimentally for both Pb and Bi. The comparison of these results with the corresponding theoretical estimates have been done only for Pb as the emission rates for various M x-ray transitions of Bi are not available in the literature. The comparison of the cross sections show fair agreement with the PWBA-based theoretical values, while there are discrepancies of a factor of 10 and 20 in the cases of and x-ray transitions.

Charge state dependence of copper L-shell x-ray production by 4 - 14 MeV oxygen ions

Charge state dependence of L-shell x-ray production cross sections in bombarded by 4 - 14 MeV ions with charge states from q = 3+ to 8+ was measured using a Si(Li) x-ray detector with a resolution of 96 eV at 1 keV. An ultra-thin copper foil was used to ensure single-collision conditions. The data for the total L x-ray production cross sections are compared to the predictions of the first Born and the ECPSSR calculations for L-shell ionization converted to x-ray production cross sections using a single-hole fluorescence yield. Except at the lowest projectile velocity, the ECPSSR theory gives satisfactory agreement with the data while the first Born theory overpredicts all the data in the investigated energy range by almost two orders of magnitude. Measurements of the charge state dependence of the target L-shell x-ray production cross sections allowed the separate contributions of the electron capture (EC) and the direct ionization (DI) to the inner-shell ionization to be determined. The EC contributions were extracted from the x-ray measurements with two, one, and no K-shell vacancies in the oxygen ions. These EC cross sections are compared with the results of an OBK approximation and the ECPSSR theory, and found to be significantly smaller than both EC calculations.

Deviations of 16O-induced K X-ray yields from Z12 dependence

A careful comparison of K X-ray yields produced by 64 MeV 16O ions and 4 MeV protons of identical velocity has been carried out with ±2% precision, using thin (∼ 10 nm) targets of Ti, Cr and Ag. The incident oxygen charge state was varied from 6+ to 8+. Since the path length for charge exchange in the K-shell of oxygen greatly exceeds our target thickness, the effective 16O charge state is essentially equal to its incident value. For the highest- Z 2 target (Ag), our O 6+, 7+ and 8+ yields were identical (to ± 2%) but were only 24 times the proton yield. This ratio is considerably smaller than the Z 1 2 prediction of 64, but agrees well with the factor of 28 predicted by the ECPSSR theory. The lack of dependence on charge state indicates that electron capture into the K-shell of oxygen is negligible when Z 2 ⪡ Z 2. For the lower- Z 2 targets, a strong dependence on charge state is observed. Moreover, the measured O 8+ enhancement factor relative to 4 MeV protons is 125 in Ti, i.e., twice the simple Z 1 2 scaling value. Again, these observations are well reproduced by the ECPSSR calculations and the major cause of the enhanced O 7+ and O 8+ yields in Ti and Cr is electron capture into K-shell vacancies of the oxygen ion. Residual discrepancies between the X-ray yield data and the ECPSSR ionization calculations are attributed to enhancement of fluorescence yield when Z 1 Z 2 is large and the emergence of molecular orbital effects when the projectile velocity is small relative to the target's K-shell electron orbital velocity.

Measurement of M X-ray production cross sections in gold by proton, oxygen and nickel ion impact

Measurements of M-shell X-ray production cross sections in Au with proton, O 5+- and Ni 5+-ion impact have been performed. The energy of the incident protons range from 1 to 5 MeV, oxygen ions from 66 to 72 MeV and nickel ions from 58 to 87 MeV. The experimental results have been compared with the predictions of the plane wave Born approximation (PWBA) and the perturbed stationary state theory with energy loss, Coulomb deflection and relativistic corrections (ECPSSR). For proton impact the measured cross sections have been found to be in good agreement with both these theories. With O-ion impact the ECPSSR theory underpredicts the experimental data while the PWBA agrees fairly well. Both the theories, however, strongly underestimate the X-ray cross sections measured with Ni-ion impact. The discrepancy between the experimentally measured and theoretically calculated cross sections in case of heavy ion impact could be due to multiple ionization which changes the values of atomic parameters like sub-shell fluorescence yields, Coster-Kronig transition probabilities and emission rates.

ISICS: A program for calculating K-, L- and M-shell cross sections from ECPSSR theory using a personal computer

A versatile and fast C-language program has been developed to exactly calculate ionization and x-ray production cross sections using the ECPSSR theory. All elements and any projectile can be selected for any range of energies and energy increments. Coulomb excitation form factors are numerically calculated in the program. Comparisons are presented between program calculations and those obtained by standard procedures from other sources. The program is available in compiled form and in source code for modification by the user. User options include selecting a relativistic calculation of the projectile ion velocity. Electron capture by the projectile is not incorporated into the program at this time.

K-shell ionization of V, Cr, Mn, Fe, Co, Ni and Cu by 5–12 MeV carbon ions

The K-shell X-rays of V, Cr, Mn, Fe, Co, Ni and Cu induced by 12C ions were detected in the projectile energy range 5–12 MeV. From these measurements, experimental K-shell X-ray production cross sections; K α, K β X-ray energy shifts and the K α K β intensity ratios are extracted and presented. Our results are compared with the experimental data obtained previously and with the predictions of the perturbed stationary-state approximation with energy loss, Coulomb, and relativistic corrections (ECPSSR theory). The role of electron transfer to the projectile have been discussed.

Charge-state dependence of K-shell x-ray production in aluminum by 2-12-MeV carbon ions.

Charge-state dependence for {ital K}-shell x-ray production cross sections in {sub 13}Al bombarded by 2{endash}12-MeV {sub 6}C ions with charge states from 2+ to 6+ was measured using a Si(Li) detector. A thin Al target was used to ensure single collision conditions. Contributions of the electron capture as well as direct ionization to the inner-shell ionization were determined by an analysis of the charge-state dependence of the target x-ray production. The measurements are compared with the prediction of the ECPSSR theory using a single-hole fluorescence yield. The ECPSSR theory is based on the perturbed stationary state (PSS) formalism and relativistic effects (R) for the target electrons, and energy loss (E) and Coulomb deflection (C) of the projectile. In general, this theory gives reasonable agreement with the data for carbon ions without {ital K} vacancies while it overpredicts the data for carbon ions with {ital K} vacancies. The significant underprediction of the data at the lowest energy is likely associated with the molecular-orbital effect that is not accounted for in the ECPSSR theory. {copyright} {ital 1996 The American Physical Society.}

L-subshell ionization of Eu, Gd and W by 1.6–5.2 MeV protons

L-shell X-rays for Eu, Gd and W were measured in the proton energy range from 1.6 to 5.2 MeV. From these measurements, individual X-ray production cross sections, together with the cross section ratios L α /L β and L α /L γ were calculated. L 1, L 2 and L 3 subshell ionization cross sections were extracted from the X-ray production cross sections for L γ2,3, L γ1,5 and L α1,2 X-ray lines. The results are compared with the experimental data published by other authors and with the theoretical predictions of the ECPSSR theory.

M-shell X-ray production by C, N and O ions

M-shell X-ray production cross sections for Os, Au and Th targets were measured for C, N and O ions at incident energies from 1.2 MeV to about 36 MeV. Experimental M-shell ionization cross sections, derived by using the effective M-shell fluorescence yields, are compared with the prediction of the SCA calculations with relativistic hydrogenic wave functions. The calculations were performed both in the separated-atom (SA) and united-atom (UA) limits to simulate the binding effect. Generally, the data show better agreement with the SCA-UA cross sections for lower energies and with the SCA-SA predictions for higher energies. For C and O impact on the Au target at about 2 MeV/amu the present data are compared with available experimental results and theoretical predictions of the ECPSSR theory.