L-subshell Ionization Research Articles

Collision-induced atomic alignment of silver after [formula omitted] ionization by 10–50 keV electron impact: Influence of Coster–Kronig transition effect

This work reports atomic alignment of silver after L3-subshell ionization in collisions with electrons in energy range 10–50 keV, i.e., (3∼15)EL3, where EL3(=3.351 keV) is the binding energy of electrons in the L3-subshell. The characteristic spectra are measured at different emission angles from -40∘ to 40∘ intervals of 10∘. The angular dependence of X-ray emission is studied for Lα(L3→M4,5) and Lβ2(L3→N5) lines respectively, using a thin target. The anisotropy parameter β is determined from two angular distribution measurements of differential X-ray intensity ratios dI(Lα,θ)/dI(Lβ1,θ) and dI(Lβ2,θ)/dI(Lβ1,θ). This served to reduce the experimental uncertainties. For the derivation of the alignment factor A20 we took into account the Coster–Kronig (CK) correction factor κ, which allows for, CK transition probabilities fij among L-subshells. We found that the sign of A20 is mostly negative, and the influence of CK transition is significant for large alignment parameters. In addition, the experimental results are compared to theoretical predictions within the framework of Plane Wave Born Approximation (PWBA) and reasonable agreement is found in the energy range studied in the present work. Simultaneously, good scaling property of atomic alignment is demonstrated when we consider also previous experimental results. Our measurement extends the scaled velocity V (=vp/vt) to a range of 1∼4 for medium-Zt targets, and the results of atomic alignment can provide a fundamental testing ground for ionization models.

L-Shell Ionization Cross Sections for Silver by Low-Energy Electron Impacts

The L-subshell ionization cross sections and total L–X-ray production cross sections for the Ag atom by the electron impact near the ionization threshold were calculated with a classical-trajectory Monte Carlo method. The results were compared with experimental data, quantum mechanical calculations, and the cross sections by positron impact. It was demonstrated that the classical treatments are useful for electron–atom collisions at energies higher than about six times the binding energies of target electrons but overestimate L-shell ionization and L–X-ray production cross sections at low energies near the threshold. Possible reasons for this discrepancy are discussed.

Understanding the mechanisms of L-shell x-ray emission from Os atoms bombarded by 4–6 MeV/u fluorine ion

The L-subshell ionization mechanism is studied in an ultra-thin Os target bombarded by 4–6 MeV/u fluorine ions. Multiple ionization effects are considered through the change of fluorescence and Coster-Kronig yields while determining L-subshell ionization cross sections from L x-ray production cross sections. The present experimental values are compared with various theoretical approximations: (i) the relativistic semi-classical approximation (RSCA), (ii) the shellwise local plasma approximation (SLPA), and (iii) the ECUSAR theory. We also take into account the vacancy sharing among the subshells by the coupled-states model (CSM) and the electron capture (EC) by a standard formalism. We find that the ECUSAR-CSM-EC describes the measured excitation function curves the best. However, the theoretical calculations are still about a factor of two smaller than the measured values even though the recent fluorescence and Coster-Kronig yields are considered. Hence, a re-evaluation of these parameters is a challenge for the theoretical works. Whatsoever, this work leads to demonstrate that in the present energy range the heavy-ion induced inner-shell ionization of the heavy atoms can be understood by combining the direct Coulomb ionization, the electron capture, and the vacancy sharing among subshells, together with optimizing the atomic parameters. Optimization of the atomic parameters shows that our experimental results agree with theoretical vacancy production theories if the L1 fluorescence yield is nearly doubled. Such a optimization is validated by the proton induced L-shell ionization data of uranium atoms.

Evaluation of accurate uncertainty of measurement of L subshell ionization cross-sections

Experimentally, X-ray production cross-sections are measured, but ionization cross-sections are calculated theoretically. The uncertainty of the measured L X-ray production cross-section is mainly statistics and detector-efficiency driven. But the experimental ionization cross-section involves many other factors because the relationship between the production and ionization cross section involves various atomic parameters and thus its uncertainty equation is complex. Consequently, determining the measurement uncertainty in L subshell ionization cross-section is always difficult. We have studied this issue in the simplest way, where the rule of weighted propagation of relative uncertainty is utilized. We notice that larger uncertainties are involved in atomic parameters relevant to L1 (2s1/2) subshell than those associated with the other two L2 (2p1/2) and L3 (2p3/2) subshells. Hence, comparison between theory and experiment would give higher emphasis on L2 and L3 subshell ionization cross sections. We believe this work makes us aware that the appropriate uncertainty evaluation is extremely important for providing the right judgement on the data.

Electron impact L-subshell and total L-shell ionization cross-sections of atoms (Z = 18–92)

We propose an extension of the modified Vaisburd and Evdokimov model (MVE) (2003 Russ. Phys. J. 46 1160) incorporating the relativistic effects to investigate the L1-, L2- and L3-subshells as well as total L-shell ionization cross-sections (LSICS) of atomic targets with atomic numbers 18 ≤ Z ≤ 92 for incident energies upto 1 GeV. We also revisited our earlier XMUIBED and XMCN model for individual L-subshell ionization cross-sections and MUIBED, GKLV and XCVTS for total LSICS for 28 atomic targets. We compare our new results from the MVE model with the available experimental data and other calculations including our previously proposed models.

Ionization cross sections of the Au L subshells by electron impact from the L3 threshold to 100 keV

We measured the cross sections for Au Lα, Lβ, Lγ, Lℓ and Lη x-ray production by the impact of electrons with energies from the L3 threshold to 100 keV using a thin Au film whose mass thickness was determined by Rutherford Backscattering Spectrometry. The x-ray spectra were acquired with a Si drift detector, which allowed to separate the components of the Lγ multiplet lines. The measured Lα, Lβ, , L, , , and Lη x-ray production cross sections were then employed to derive Au L1, L2 and L3 subshell ionization cross sections with relative uncertainties of 8%, 7% and 7%, respectively; these figures include the uncertainties in the atomic relaxation parameters. The correction for the increase in electron path length inside the Au film was estimated by means of Monte Carlo simulations. The experimental ionization cross sections are about 10% above the state-of-the-art distorted-wave calculations.

Use of the Bethe Equation for Inner-Shell Ionization by Electron Impact.

We analyzed calculated cross sections for K-, L-, and M-shell ionization by electron impact to determine the energy ranges over which these cross sections are consistent with the Bethe equation for inner-shell ionization. Our analysis was performed with K-shell ionization cross sections for 26 elements, with L-shell ionization cross sections for seven elements, with L3-subshell ionization cross sections for Xe, and with M-shell ionization cross sections for three elements. The validity or otherwise of the Bethe equation could be checked with Fano plots based on a linearized form of the Bethe equation. Our Fano plots, which display theoretical cross sections and available measured cross sections, reveal two linear regions as predicted by de Heer and Inokuti. For each region, we made linear fits and determined values of the two element-specific Bethe parameters. We found systematic variations of these parameters with atomic number for both the low- and the high-energy linear regions of the Fano plots. We also determined the energy ranges over which the Bethe equation can be used.

L-shell ionization cross sections for silver by electron impact

SynopsisThe L-subshell ionization cross sections by electron impact have been calculated with the classical-trajectory Monte Carlo method. The results are compared with the quantum mechanical calculations and the cross sections by positron impact. It is demonstrated that the classical treatments are quite useful for electron-atom collisions.

Ionization cross sections of the L subshells of Au by 50 to 100 keV electron impact

We have measured the Lα, Lβ, , , L, and Lη x-ray production cross sections of Au by 50–100 keV electron impact. From this experimental information we derived the L1, L2 and L3 subshell ionization cross sections with a novel analysis procedure that is based on an overdetermined system of equations and achieve the estimates by the least-squares method. The uncertainties in the atomic relaxation parameters needed to transform the x-ray intensities to ionization cross sections impose a lower limit to the relative standard deviations of the L subshell ionization cross sections, which is found to be 5–10% depending on the selected set of relaxation parameters. Our experimental results are in reasonable accord with most of the measurements carried out by other authors, and they agree with the predictions of the semi-relativistic distorted-wave Born approximation.

Cross Sections for Inner-Shell Ionization by Electron Impact

An analysis is presented of measured and calculated cross sections for inner-shell ionization by electron impact. We describe the essentials of classical and semiclassical models and of quantum approximations for computing ionization cross sections. The emphasis is on the recent formulation of the distorted-wave Born approximation by Bote and Salvat [Phys. Rev. A 77, 042701 (2008)] that has been used to generate an extensive database of cross sections for the ionization of the K shell and the L and M subshells of all elements from hydrogen to einsteinium (Z = 1 to Z = 99) by electrons and positrons with kinetic energies up to 1 GeV. We describe a systematic method for evaluating cross sections for emission of x rays and Auger electrons based on atomic transition probabilities from the Evaluated Atomic Data Library of Perkins et al. [Lawrence Livermore National Laboratory, UCRL-ID-50400, 1991]. We made an extensive comparison of measured K-shell, L-subshell, and M-subshell ionization cross sections and of Lα x-ray production cross sections with the corresponding calculated cross sections. We identified elements for which there were at least three (for K shells) or two (for L and M subshells) mutually consistent sets of cross-section measurements and for which the cross sections varied with energy as expected by theory. The overall average root-mean-square deviation between the measured and calculated cross sections was 10.9% and the overall average deviation was −2.5%. This degree of agreement between measured and calculated ionization and x-ray production cross sections was considered to be very satisfactory given the difficulties of these measurements.

Measurement of L X-Ray relative intensities for selected heavy elements

The L-shell X-ray relative intensities I(Ll/Lα), I(Lβ/Lα) and I(Lγ/Lα) for Ba, Pr, Pt, Hg, and Bi, have been measured at the excitation energy of 20.48keV. Measurements have been performed using a system that consists of X-ray tube as an excitation source and Si(Li) detector. Theoretical values of the relative intensities have been calculated using theoretical values of L-subshell ionization cross-sections, L-subshell fluorescence yields, Coster–Kronig probabilities and fractional X-ray emissions. Experimental results have been compared with the theoretically calculated values. The measured values showed reasonable agreement with theoretical values.

Updated database for L x‐ray production by protons and extraction of L‐subshell ionization cross sections from only Lγ and Lα + Lβ cross sections

AbstractDatabase from pre‐1995 compilations of L x‐ray production and ionization by protons is enlarged by 53% with the present update. Semiempirical formulas for Lγ and Lαβ are developed and used to extract L1, L2, and L3 subshell ionization cross sections. The extracted ionization cross sections are shown for a sample of elements and compared with the database ionization cross sections in gold. Copyright © 2011 John Wiley & Sons, Ltd.

New data base for Lα, Lβ, Lγ x-ray production by protons, new empirical fits, extraction of L-subshell ionization cross sections with various atomic parameters, and their comparison with the ECPSSR theory and its modifications: a recommendation for reliable choice of atomic parameters and ionization theory for PIXE analysis

Tables of L-shell and L-subshell x-ray production cross sections by protons from 1994 are updated, and the so constructed data base is fitted to formulas for empirical Lα, Lβ, Lγ x-ray production cross sections. Based on these fits, empirical L-subshell ionization cross sections are generated with various sets of atomic parameters with and without alteration for multiple ionizations. The extracted ionization cross sections are compared with the predictions of the ECPSSR theory and it modifications. Based on comparisons with different choice of the atomic parameters and theories, we will recommend an optimal combination of the atomic parameters and ionization theory for a reliable input in PIXE applications software.

L-subshell ionization of heavy elements by S ions with energy of 0.4–3.8 MeV/amu

The L-shell X-ray production cross sections have been measured for sulphur ions in the energy range of 12.8–120MeV for Au and Bi elements. The experimental L X-ray spectra were analyzed using the method that takes into account the multiple ionization in outer shells. The L-subshell ionization cross sections have been obtained from measured X-ray production cross sections for resolved Lα1,2 Lγ1 and Lγ2,3 transitions using the L-shell fluorescence and Coster–Kronig yields modified by the multiple ionization effects in the M and N shells. The results are compared with the predictions of ECUSAR theory, which is the modified ECPSSR approach describing both direct ionization and electron-capture processes and the semiclassical approximation (SCA) calculations for direct ionization. These approaches were modified by the L-subshell coupling effects within the “coupled-subshell model” (CSM). Both modified approaches are in good agreement with the data. Remaining discrepancies are discussed in terms of the L-shell decay rates modified for the multiple ionization effects.

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.

Coupling and binding effects in L-shell ionization of heavy atoms by oxygen, silicon and sulphur ions

The coupling and binding effects in ionization of L-shell electrons by heavy ions have been studied by measuring the Lγ(L–N,O) X-ray transitions in gold excited by an impact of O, Si and S ions in the energy range 0.3–5MeV/amu. The L-subshell ionization cross sections were extracted from measured X-ray spectra taking into account their substantial modifications due to the multiple ionization effects, which also change the fluorescence and Coster–Kronig yields. In order to interpret the data the L-subshell couplings were incorporated in the theoretical calculations based on the semiclassical approximation (SCA) within the “coupled subshell model” (CSM). Resulting SCA–CSM calculations, which describe the data for oxygen ions quite satisfactory, are further modified to include the saturation of the binding effect in order to describe the data for heavier Si and S ions. We find that the semiclassical SCA–CSM calculations of L-shell ionization by heavy ions (Z1≫1), which include corrections both for coupling and binding saturation effects, agree reasonably well with the measured data.

L1, L2 and L3 subshell ionization cross sections for elements with 71 ⩽ Z ⩽ 80 for protons of 0.5 to 3.0 MeV

We present in this contribution theoretical predictions of the L i (i = 1, 2, 3) subshells ionization cross sections within the ECPSSR theory for elements with atomic number 71 ⩽ Z ⩽ 80 for protons with energy of 0.5 to 3.0 MeV. These predictions are compared to the experimental data reported by Orlic et al. [At. Data Nucl. Data Tables 56 (1994) 159] and by Sokhi and Crumpton [At. Data Nucl. Data Tables 30 (1984) 49] by plotting the ratio S = σ exp/ σ ECPSSR as a function of the reduced velocity parameter for each individual subshell L1, L2 and L3. By fitting separately the ratio S, we deduced reference ionization cross sections for each Li subshell. On the other hand, we report empirical ionization cross sections and make a comparison between the reference cross sections, the empirical cross sections reported in this paper and those reported by Sow et al. [Nucl. Instr. and Meth. B 75 (1993) 58] and by Orlic et al. [Int. J. PIXE 4 (4) (1994) 217]

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.

The role of multiple ionization and subshell coupling effects inL-shell ionization of Au by oxygen ions

The ionization of L-subshell electrons in gold by the impact of0.4-2.2 MeV amu-1 O ions was studied by observing excitedLγ(L-N, O) x-rays. We demonstrate that both the multipleionization in outer M- and N-shells as well as the couplingeffects in the L-shell play an important role in understandingthe measured L-subshell ionization cross sections. The multipleionization was found to be important in two aspects: first, theanalysis of x-ray energy shifts and line broadening was crucialfor proper interpretation of measured x-ray spectra; second,the additional vacancies in the M- and N-shells substantially influenced the L1-subshell fluorescence and Coster-Kronig (CK)yields, mainly by closing strong L1-L3M4,5 CKtransitions. The data are compared with the simplifiedcoupled-channels calculations using the `coupled-subshell model'(CSM) based on the semiclassical approximation (SCA), whichdescribes both direct Coulomb ionization as well as theL-subshell couplings within the same theoretical approach. Agood agreement of the present data with the theoreticalpredictions based on the discussed SCA-CSM approach is observed.Present findings partly explain the long-standing problem ofinadequate theoretical description of L-shell ionization byheavy ion impact.

Spin asymmetry in weakly relativistic(e,2e)collisions

Two geometries are chosen to make predictions and to test the Coulomb-Born approximation against the distorted-wave Born approximation and experiment, the symmetric coplanar constant ${\ensuremath{\Theta}}_{12}$ geometry for K-shell ionization of Ag and the asymmetric coplanar geometry for L-subshell ionization of U. Even for the heaviest target, good agreement is found as long as the two electrons emerge on opposite sides of the beam axis.