Coulomb Deflection Effects Research Articles

Perturbation on atomic alignment of Ag L3-subshell by multiple ionization for heavy ions impact

Alignment of silver ion after electron in L3-subshell ionized by 1H+, 4He2+, 40Ar12+ and 129Xe30+ ions impact respectively are reported. Low incident energy range is investigated to explore collision-induced alignment in case of strong Coulomb deflection effect. Characteristic L X-ray spectra are measured in emission angle range of 115∘-155∘. For Lα and Lβ2 lines, anisotropy parameter β is determined respectively and then converted to degree of alignment A20 by taking anisotropy coefficient α and Coster-Kronig (CK) correction coefficient κ into account. The measured atomic alignment is compared to theoretical prediction basing on semiclassical model and satisfactory agreement is observed only for light ions impact. While the dealignment coefficient is determined to be 0.98, 0.71 and 0.30 for 4He2+, 40Ar12+ and 129Xe30+ ions impact at (vp/vL3)2=0.011, respectively. This work demonstrates the strong dealignment due to multiple ionization for heavy ions impact even in ultra low incident energy regime.

M X‐ray production cross sections for heavy elements by proton impact

AbstractWe present in this paper, M‐shell ionization cross sections and M X‐ray production cross sections calculated within the Energy loss, Coulomb deflection, Perturbed Stationary State and Relativistic effects (ECPSSR) theory for elements with 72 ≤ Z ≤ 90 for protons with 0.1–4.0 MeV energy. Our results are compared to the plane wave Born approximation (PWBA) predictions, the relativistic plane‐wave Born approximation including corrections for binding and Coulomb deflection effect (RPWBA‐BC) results and the ECPSSR calculations from earlier works. On the other hand, semiempirical and empirical M X‐ray production cross sections are deduced from the polynomial fitting of the available experimental data collected from different sources. A comparison is made between the different sets of results. The differences between the above calculations and the experimental results are pointed out and discussed. Copyright © 2009 John Wiley & Sons, Ltd.

A ionization theory based on united and separated atom model

The direct Coulomb ionization process can be generally well described by the ECPSSR theory, which bases on the perturbed-stationary-state(PSS) and accounts for the energy-loss, Coulomb-deflection, and relativistic effects. But the ECPSSR calculation has significant deviations for heavy projectile at low impinging energies. In this paper we propose a new modified ECPSSR theory, i.e. MECUSAR, in which PSS is replaced by an united and separated atom model, and molecule-orbit effect is considered. The MECUSAR calculations give better agreement with the experimental data at lower impinging energies, and agree with the ECPSSR calculations at high energies. By using OBKN (Oppenheimer-Brinkman-Kramers formulas of Nikolaev) theory to describe the contribution of the electron capture, we further modified the proposed MECUSAR theory, and calculated the target ionization cross sections for different charge states of the projectile.

TargetK-vacancy production by2.5to25MeV∕amuAr, Kr, and Xe ions

Cross sections have been measured for $K\ensuremath{\alpha}$ x-ray production in targets of Al, Ti, Cu, Zr, Ag, Sm, and Ta by Ar, Kr, and Xe ions ranging in energy from $2.5\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}25\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{amu}$. In addition, the degree of simultaneous $L$-shell ionization and the enhancement of the $K\ensuremath{\alpha}$ diagram lines due to secondary ionization processes were assessed by performing high-resolution spectral measurements on Al, Ti, V, Co, and Cu targets. This information was used to correct for the $K\ensuremath{\alpha}$ x-ray yield produced by electron bombardment and photoionization, and to calculate the fluorescence yields needed to convert the $K\ensuremath{\alpha}$ x-ray production cross sections into $K$-vacancy production cross sections. The resulting cross sections were compared with the predictions of the perturbed stationary state approximation with corrections for projectile energy loss, Coulomb deflection, and relativistic effects (ECPSSR theory). Also, the scaling properties of the $K\ensuremath{\alpha}$ x-ray production cross sections were examined and a semiempirical (universal) curve was deduced that reproduces the measured cross sections to within $\ifmmode\pm\else\textpm\fi{}30%$ on average.

Projectile atomic number dependence of the relativistic effect on theK-shell ionization of highZelements under heavy-ion impact

Absolute $K$-shell ionization cross sections of Sb, Au, and Bi have been measured in collisions with highly charged C, O, and S ions having energies between 2 and $6.25\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕u$. The data are presented along with the earlier results with F and Si ions as projectiles. The measured data have been compared with theoretical models based on the semiclassical approximation including relativistic effect and perturbed stationary state approximation including the corrections for energy loss, Coulomb deflection, and relativistic effects. The data were analyzed in term of relativistic effect on $K$-ionization: its dependence on the projectile atomic number, target atomic number and projectile energy. The present data set along with our recently measured similar data for F and Si ions show that the relativistic effect increases with projectile atomic number and decreases with projectile velocity. A comparison of the experimental data and relativistic calculations, both normalized to nonrelativistic model, show the inadequacy of the theoretical models in describing the relativistic correction on $K$-shell ionization. For example, the theoretical predictions agree with experimental findings for O ions on Bi while the same theoretical predictions deviate from the experimental results by about a factor of 2 for Si and S on Bi, the theory being higher.

L-subshell ionization of Ce, Nd, and Lu by4–10−MeVC ions

$Ll,L\ensuremath{\alpha},L\ensuremath{\beta},L\ensuremath{\gamma},L{\ensuremath{\gamma}}_{1+5},L{\ensuremath{\gamma}}_{2+3},L{\ensuremath{\gamma}}_{4+{4}^{\ensuremath{'}}}$ x-ray production cross sections of $_{58}\mathrm{Ce}$, $_{60}\mathrm{Nd}$ and $_{71}\mathrm{Lu}$ induced by 4-, 6-, 8-, and $10\text{\ensuremath{-}}\mathrm{MeV}$ carbon ions were measured. For Lu, $L{\ensuremath{\gamma}}_{2+3}$ is separated from $L{\ensuremath{\gamma}}_{2+3+6}$ after revision of the technique of Datz et al. so that $L{\ensuremath{\gamma}}_{1+5}$ was used instead of $L{\ensuremath{\gamma}}_{1}$, the $L{\ensuremath{\gamma}}_{4+{4}^{\ensuremath{'}}}∕L{\ensuremath{\gamma}}_{1+5}$ ratio was corrected for multiple ionization, and uncertainties in $L{\ensuremath{\gamma}}_{4+{4}^{\ensuremath{'}}}$ were incorporated in the fitting process. $L$-subshell ionization cross sections were extracted as a weighted average from two combinations of these cross sections, ${L\ensuremath{\alpha},L{\ensuremath{\gamma}}_{1+5},L{\ensuremath{\gamma}}_{2+3}}$ and ${L\ensuremath{\alpha},L{\ensuremath{\gamma}}_{1+5},L\ensuremath{\gamma}}$. It is shown that, to within a few percent, the first of these two combinations results in the identical cross sections as this weighted average. Within 10%, permutations of different sets of single-hole atomic parameters yielded the same ionization cross sections. These cross sections are typically within 15% and at most 35% of the cross sections obtained with atomic parameters that were altered in two different ways for multiple ionization. Extracted subshell and total $L$-shell ionization cross sections as well as Ce and Nd data of Braziewicz et al. are compared with the ECPSSR theory of Brandt and Lapicki that accounts for the energy-loss (E), Coulomb-deflection (C), perturbed-stationary-state (PSS) and relativistic (R) effects. These measurements are also compared with the ECPSSR theory after its corrections---in a separated and united atom (USA) treatment, and for the intrashell (IS) transitions with the factors of Sarkadi and Mukoyama normalized to match $L$-shell cross section with the sum of $L$-subshell cross sections---as well as with the similarly improved semiclassical approximation of Trautmann. For Ce and Nd, the agreement of the extracted ionization cross sections with these theories is poor for ${L}_{1}$ and good for ${L}_{2}$, ${L}_{3}$, and total $L$ shell ionization. For the ${L}_{2}$ subshell, this agreement is better for Ce and Nd than for Lu. The ECPSSR theory corrected for the USA and IS effects is surprisingly good for the ${L}_{1}$-subshell ionization of Lu, while at $4\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ a similarly corrected semiclassical approximation is in excellent agreement with ${L}_{2}$ and ${L}_{3}$ data but overestimates the ${L}_{1}$ measurement by almost a factor of 2.

M X-ray production in Nd, Gd, Ho and Lu by 1–6 MeV lithium ions

M-shell X-rays of the rare-earth elements 60Nd, 64Gd, 67Ho and 71Lu were measured for lithium ion bombardment in the energy range 1.0–6.0 MeV. The M-shell X-rays with energies of 0.978–1.631 keV were detected with a LINK analytical detector. The efficiency of the detector was determined by using the known atomic-field bremsstrahlung cross-sections from low energy electron beams and K-shell X-ray measurements with light projectiles. The measured cross-sections are compared to the predictions of the first Born approximation and the ECPSSR (energy loss and Coulomb deflection effects, perturbed stationary state approximation with relativistic correction) theories. The best theoretical description of the present data is given by the ECPSSR theory, even though the discrepancy between data and theory is increasing at higher projectile energies.

Multiple ionization and coupling effects inL-subshell ionization of heavy atoms by oxygen ions

The multiple-ionization and coupling effects in L-shell ionization of atoms by heavy-ion impact have been studied by measuring the L x-ray production cross sections in solid targets of Au, Bi, Th, and U bombarded by oxygen ions in the energy range 6.4--70 MeV. The measured L x-ray spectra were analyzed using the recently proposed method accounting for the multiple-ionization effects, such as x-ray line shifting and broadening, which enables one to obtain the ionization probabilities for outer shells. The L-subshell ionization cross sections have been obtained from measured x-ray production cross sections for resolved $L{\ensuremath{\alpha}}_{1,2},$ $L{\ensuremath{\gamma}}_{1},$ and $L{\ensuremath{\gamma}}_{2,3}$ transitions using the L-shell fluorescence and Coster-Kronig yields being substantially modified by the multiple ionization in the M and N shells. In particular, the effect of closing of strong ${L}_{1}\ensuremath{-}{L}_{3}{M}_{4,5}$ Coster-Kronig transitions in multiple-ionized atoms was evidenced and discussed. The experimental ionization cross sections for the ${L}_{1},$ ${L}_{2},$ and ${L}_{3}$ subshells have been compared with the predictions of the semiclassical approximation (SCA) and the ECPSSR theory that includes the corrections for the binding-polarization effect within the perturbed stationary states approximation, the projecticle energy loss, and Coulomb deflection effects as well as the relativistic description of inner-shell electrons. These approaches were further modified to include the L-subshell couplings within the ``coupled-subshell model'' (CSM). Both approaches, when modified for the coupling effects, are in better agreement with the data. Particularly, the predictions of the SCA-CSM calculations reproduce the experimental L-subshell ionization cross section reasonably well. Remaining discrepancies are discussed qualitatively, in terms of further modifications of the L-shell decay rates caused by a change of electronic wave functions in multiple-ionized atoms.

Relativistic wave-function effect on theK-shell ionization of Sb, Gd, Yb, Au, and Bi by low- to intermediate-velocity F ions

We have measured absolute cross sections for the K-shell ionization of medium- and high-Z targets of Sb, Gd, Yb, Au, and Bi induced by low- to intermediate-velocity F ions having energies between 2.5 and 5.8 MeV/u. Our main interest is to see the effect of the relativistic nature of the K-shell electrons of these target atoms on the ionization cross sections. The information on the degree of relativistic effect has been obtained by comparing the measured data with different theoretical calculations with and without including the relativistic corrections. A comparative study of the two different models such as SCA (semiclassical approximation) and ECPSSR [perturbed stationary state (PSS) including the corrections for energy (E) loss, Coulomb (C) deflection, and relativistic (R) effects] is presented. It is shown that the SCA calculations with the relativistic wave function predict an ionization cross section that is at least an order of magnitude higher compared to that given by the nonrelativistic calculation for Bi target. This factor is reduced to about 2 in the case of Sb. The ECPSSR, however, predicts lower ratios for the relativistic to nonrelativistic calculations. The experimental results, in general, are in good agreement with the SCA calculations using relativistic wave functions as well as with the ECPSSR model. For high-Z targets the SCA gives slightly better agreement with the data compared to the ECPSSR. In addition, it is shown that in the ECPSSR formalism the ionization cross sections of high-Z (with large relativistic effect) as well as low-Z targets (with less relativistic effect) can be scaled approximately to follow a universal curve after including the relativistic 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.

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.

L-shell ionization in Au by O5+-and Ni5+-ion impact

TheL X-ray production cross sections in gold by 60 to 72 MeV O5+ ions and 58 to 87 MeV Ni5+-ions have been measured. TheL-subshell ionization cross sections derived from these experimental results have been compared with the direct ionization theories viz. plane wave Born approximation (PWBA) theory and modified perturbed-stationary-state theory with energy loss, Coulomb deflection and relativistic effects (MECPSSR). A new procedure has been described to account for the change in the yield ratioLβ1/Lβ2, 15 with energy, for Ni5+-ion impact on gold. TheL sub-shell ionization cross sections have been derived fromLβ1,Lβ4 andLβ2, 15 lines of theLβ group in addition to those calculated by the conventional Datz TRY3 technique usingLα,Lγ1 andLγ2, 3 X-ray lines. From the shift in the energies of variousL X-ray lines and changes in their intensities, 3 and 5 spectator vacancies in theM- andN-shells in gold have been estimated with O5+-ion impact while 7, 20 and 4 to 6 spectator vacancies have been inferred in theM-,N-andO-shells respectively with Ni5+-ion impact in the energy range of the projectiles undertaken in the present studies.

L X-ray production in La, Nd, Gd, Er and Lu by 1-5 MeV protons

Cross sections for production of Lalpha , Lbeta , Lgamma and Ll X-rays in lanthanum, neodymium, gadolinium, erbium and lutetium were measured with proton bombardment in the energy range 1-5 MeV. These cross sections and their ratios are found to be, in general, in good agreement with the ECPSSR (energy loss and Coulomb deflection effects, perturbed stationary state approximation with relativistic correction) theory.

A STUDY ON THE BEHAVIOR OF THE ALIGNMENT FOR L3 VACANCY STATE IN Au BY IMPACT IONISATION

In low projectile energy region, the alignment of L3 vacancy state in Au and the projectile energy dependence of alignment were measured for several kinds of ions and Au collision systems by a simple method. Using the plane-wave Born approximation (PWBA) and taking into account the coulomb deflection effect, the alignment was calculated. It is shown that the present calculated results are closer to the experimental data. The alignment behavior of L3 vacancy state in Au is furtherly discussed.

L-shell X-ray production cross sections for 29Cu, 31Ga, 32Ge, 35Br, 39Y, 60Nd, 64Gd, 67Ho, 70Yb, 79Au, and 82Pb for 2–25 MeV carbon ions

Measurements of L-shell X-rays in selected elements produced by carbon ions of 2–25 MeV are presented. The energies of the X-rays under consideration range from about 1 to 15 keV. The Si(Li) detector efficiency at these X-ray energies was determined using multiple normalization techniques. These methods include measuring i) the bremmstrahlung spectral distribution and ii) K-shell X-rays and normalizing to the cross sections of the ECPSSR (energy-loss and Coulomb deflection effects, perturbed stationary state approximation with relativistic correction) theory. Using single-hole fluorescence yields, the measured cross sections are compared to the predictions of first Born and ECPSSR theories. In general results compare favorably to the ECPSSR theory.

M-shell X-ray production cross sections of rare-earth elements by 4He 2+ impact in the energy range 0.7–7.0 MeV

M-shell X-rays of the rare-earth elements 57La, 60Nd, 62Sm, 63Eu, 64Gd, 66Dy, 67Ho, 66Dy, 67Ho, 68Er, 70Yb, 71Lu, and 72Hf were measured for 4He 2+ bombardment in the energy range 0.7–7.0 MeV. The M-shell X-rays with energies of 0.64–1.90 keV were detected with a windowless Si(Li) detector. The efficiency of the detector was determined by using the known atomic-field bremsstrahlung cross sections from low energy electron beams, K-shell X-ray measurements with light projectiles, and calibrated radioactive sources. The measured cross sections are compared to the predictions of the first Born approximation and the ECPSSR (energy loss and Coulomb deflection effects, perturbed stationary state approximation with relativistic correction) theories.

K-shell-ionization cross sections for low-Z elements (11

K-shell-ionization cross sections for Na, Mg, Al, Si, Cl, K, Ca, and Ti by protons in the energy range 0.5--2.5 MeV have been measured using thin targets. Measurements have also been performed for thin targets of Fe, Ni, and Cu at a few energies. The energy range of protons for these targets corresponds to the reduced velocity (${\mathit{v}}_{1}$/${\mathit{v}}_{2\mathit{K}}$) range 0.2--1.1, in which the cross sections are very sensitive to the increased binding energy and the Coulomb-deflection effects. The measured ionization cross sections are compared with the predictions of the theory based on the perturbed-stationary-state approach including the Coulomb-deflection, energy-loss, and relativistic corrections. The data have been scaled according to various scaling laws to test the validity of the universal nature of the various Coulomb ionization theories based on the plane-wave Born approximation, the binary-encounter approximation, and the simplified semiclassical approximation model as given by L\ae{}gsgaard, Andersen, and Lund [in Proceedings of the Tenth International Conference on the Physics of Electronic and Atomic Collisions, edited by G. Watel (North-Holland, Amsterdam, 1978), p. 353]. The measured data have also been compared with the calculations of Montenegro and Siguad [J. Phys. B 18, 299 (1985)] based on the theory of 1s\ensuremath{\sigma} molecular-orbital ionization.

K-shell x-ray production in 6C, 8O, 9F, 11Na, 12Mg, and 13Al by 0.5-8.0-MeV helium ions.

K-shell x-ray production cross sections are reported for incident $^{4}\mathrm{He}$ ions for elements with K-shell binding energies between 277 eV (C) and 1487 eV (Al). The data are compared with the first-order Born approximation (plane-wave Born approximation for direct ionization and Oppenheimer-Brinkman-Kramer approximation for electron capture) and to the energy loss and Coulomb deflection effects, perturbed stationary-state approximation with relativistic correction (ECPSSR) theory. The energy of the helium ions ranged from 0.5 to 6.0 MeV for ${\mathrm{He}}^{+}$ and 6.5 to 8.0 MeV for ${\mathrm{He}}^{2+}$. The targets used in these measurements were $_{6}\mathrm{C}$,${\mathrm{}}_{8}$O, $_{9}\mathrm{F}$, $_{11}\mathrm{Na}$, $_{12}\mathrm{Mg}$, and $_{13}\mathrm{Al}$. Except for a systematic overprediction of the data at the lower projectile velocities, the ECPSSR theory is found to fit the data. The first-order Born theory is found to fit the data at higher energy, but greatly overpredicts the data at low energy.

Increased-binding effects in the L-subshell ionization of Nd, Gd, and Er by charged particles

L-subshell X-ray production cross sections of Nd, Gd and Er for incident deuterons (0.30–1.00 MeV) and α particles (0.60–2.00 MeV) were measured using standard techniques. It is possible to isolate the Coulomb-deflection and increased-binding effects (which are a part of the perturbed stationary state (PSS) theoretical treatment of these phenomena) by forming ratios of the production cross sections for equal velocity pairs of incident particles (deuterons and protons for the Coulomb-deflection effect, α particles and deuterons for the increased-binding effect). The PSS theory provides a good fit to the experimental results for the Coulomb-deflection effect for all three Subshells for these same three elements [L.A. Rayburn, Nucl. Instr. and Meth. B40/41 (1989) 113]; however, it does not provide a good fit for the increased-binding effect.

INNER-SHELL IONIZATION BY LIGHT-ION IMPACT

The ECPSSR theory to calculate the inner-shell ionization cross sections by light-ion impact is studied. Starting from the general formulation of the plane-wave Born approximation, the corrections for the energy-loss effect (E) and the Coulomb-deflection effect (C) of the projectile, and for the binding-polarization effect in the perturbed-stationary-state approach (PSS) and the electronic relativistic effect (R) of the target electron are described. The calculated values in the ECPSSR theory are compared with the experimental data. In general, agreement is good, but there are systematic deviations for low-energy projectiles. The comparison with other theoretical treatments for the inner-shell ionization is discussed.