L-shell Ionization Cross Sections Research Articles

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.

Experimental and theoretical L-shell ionization cross sections of heavy atoms by impact of Si ions

We present a theoretical and experimental study of the subshell resolved L-shell ionization of relativistic targets such as 73Ta, 78Pt, 90Th, and 92U. The measurements of x-ray production cross sections by (84–140 MeV) Si+q ions (q = 8; 12), were held at the Inter-University Accelerator Centre of New Delhi. Multiple-hole fluorescence and Coster-Kronig yields were used to obtain the Li(i = 1–3) ionization cross sections from the measured x-ray production cross sections of Lℓ, Lα, and Lβ, Lη, and Lγ lines. The experimental results are compared with ab initio theoretical calculations by means of the shell-wise local plasma approximation (SLPA). This model uses the quantum dielectric formalism to obtain the total ionization cross sections from an initial ground state. The wave functions and binding energies of the different targets were obtained by solving the fully relativistic Dirac equation using the HULLAC code package. These calculations are based on first order perturbation theory with a central field, including Breit interaction and quantum electrodynamics corrections. The present SLPA ionization cross sections of the L-shell are found to be independent of the charge state of the Si ions. The experimental observations display also quite similar character if the correct mean projectile charge state inside the target is used for including the multiple ionization effect during ion-solid collisions. A general good agreement between the experimental measurements and full theoretical calculations supports the reliability of present results. The comparison also includes the well-known ECPSSR and ECUSAR semi empirical approximations. We noted that the ECUSAR results agree well with the SLPA, while the ECPSSR cross sections are rather low.

Measuring the total L-Shell X-Ray production cross sections of Te element using 6–30 keV electron impact

We report the absolute measurements of X-ray production cross sections for L-shell ionization of Te element by electron impact in an energy range of 6–30 keV with a step of 1 keV. The measurements were conducted using a scanning electron microprobe with a high-resolution X-ray silicon drift detector (SDD). The measured total L-shell X-ray production cross sections of Te were compared with the theoretical results using the distorted-wave Born approximation (DWBA) and plane-wave Born approximation with Coulomb and exchange corrections (PWBA-C-Ex). Good agreement was observed between the measured and theoretical results.

L-shell X-ray production cross sections of Ag and Au induced by carbon ions between 2 MeV and 5 MeV

In this work, we experimentally determined Ag and Au L-shell X-ray production and ionization cross sections, induced by 2–5 MeV carbon ions. The experiment was performed using the standard measurement setup already used to measure M-Shell X-ray production cross sections. Ag and Au thin targets, were used to measure L-shell X-ray spectra with Si(Li) and SDD X-ray detectors simultaneously with backscattered carbon ions from the targets by surface barrier detector. Experimental values are compared to the data available in the literature, as well as to the theoretical predictions of PWBA, ECPSSR and ECUSAR models. The analysis of data shows that the ECUSAR predictions are good at low carbon ion energies while the ECPSSR and PWBA predictions agree at the higher incident energies.

Calculated proton-induced L-shell ionisation and X-ray production cross sections for Tc, Pm, Os, Po, At, Rn, Ra and Ac

The L-shell ionisation and X-ray production cross sections of the elements: Tc, Pm, Os, Po, At, Rn, Ra and Ac, whose experimental cross sections are scanty due to their radioactive, toxic and unstable nature have been calculated. Computer codes were employed in the targets cross sections calculation for incident protons of 1.00–10.00 MeV energy range. The obtained cross sections were validated in a similar procedure for Osmium (Z2=76) induced by protons of energies 0.10–1.00 MeV and were compared with experimental data. The calculated cross sections for the Osmium target were in good agreement with the experimental data. Hence, the calculated cross sections for the considered industrially relevant targets will be a valuable addition to existing database of elements induced by protons.

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.

Calculation of L-shell ionisation and x-ray production cross sections for some trans-uranium elements induced by protons

L-shell ionisation and x-ray production cross sections of trans-uranium elements: Np, Pu and Am, induced by protons of energies 5.00–20.00 MeV, have been calculated. The cross sections for the targets were obtained using computer codes based on the ECPSSR theory. Due to the lack of experimental data of the targets considered, in view of their radioactive, toxic and unstable nature, the calculated cross sections were subsequently validated. This was achieved using the computer codes to evaluate the ionisation and x-ray production cross sections of Uranium induced by protons of energies in the 1.00–20.00 MeV range. This study also showed that the relative x-ray line intensities associated with the ionisation and x-ray productions of the targets considered are dependent on protons energies.

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.

Double effects of projectile charge state on Nb L-shell ionization by slow highly ionized Xe ions

Nb L-shell ionization cross sections induced by Xeq+ (12 ≤ q ≤ 29) ions were measured as a function of the incident charge state q in the energy ranging from 1500 to 2500 keV. In this experiment, w...

Experimental cross sections for L-shell x-ray production and ionization by protons

Tables of compiled cross sections list data for production of individual line and total L x-rays as well as for ionization of L subshells and the total L shell. The present cumulative compilation covers some six decades of measurements on targets from 10Ne to 95Am bombarded by protons ranging from 10 keV to 1 GeV. It includes data published in the period 1954–1992 from tables published in this journal, cross sections that were not reported in those tables, and new data from works published after 1992. Existing empirical, semiempirical, and theoretical analyses based on, and relative to, the pre-1993 database are reviewed. The experimental details are summarized for pre-1993 articles that were not referenced in previous compilations and, continuing the practice of these compilations, for each new publication. Covering the period 1954–December 2012, the present tabulation collects (not counting 2519 new data for Lβ1,3,4, Lβ2,15,Lγ1, Lγ2,3, and Lγ4,4′ x ray production) circa 15500 experimental cross sections and enlarges the database from the previously published tables by 94%.

Direct double L-shell ionization of a Be-like ion by a high-energy photon

We have evaluated the cross sections for the double L-shell ionization of a Be-like ion by a single high-energy photon. The evaluation is performed within the framework of non-relativistic perturbation theory with respect to the interelectron interaction. The correct linear combination of the 2s2- and 2p2-configurations is used as zeroth approximation for the wavefunction of the initial state. The interelectron interaction is taken into account between the valence electrons, while the electrons of the inner K-shell are considered as spectators. The scaling formula is obtained for the ratio of double-to-single ionization cross sections. As a by-product of our approach, we have also derived the analytical expression for the Auger width of the lowest doubly excited state of a He-like multicharged ion.

Electron impact ionization of atomic target inner-shells

There is a need for reliable theoretical methods to calculate electron-impact total ionization cross sections for the large number of neutral atoms and ions with open shell structures. These cross sections are used in a wide range of scientific and industrial applications, such as astrophysical plasmas, atmospheric science, X-ray lasers, magnetic fusion, radiation physics, semiconductor fabrication, accelerator physics and tumor therapy physics. The binary-encounter-Bethe (BEB) model [1], using an analytic formula that requires only two atomic constants, the binding energy and kinetic energy of the electrons, generates direct ionization cross sections for any neutral atom (or molecule), which are reliable in intensity (15%) and shape from the ionization threshold to a few keV in the incident energy [3], or to thousands keV if we consider its relativistic version(RBEB) [2]. In this work we present K- and L-shell ionization cross sections calculations for heavy atoms.

Analytical expression for K- and L-shell cross sections of neutral atoms near ionization threshold by electron impact

An analytical expression is proposed to describe the K- and L-shell ionization cross sections of neutral atoms by electron impact over a wide range of atomic numbers (4 ⩽ Z ⩽ 79) and over voltages U < 10. This study is based on the analysis of a calculated ionization cross section database using the distorted-wave first-order Born approximation (DWBA). The expression proposed for cross sections relative to their maximum height involves only two parameters for each atomic shell, with no dependence on the atomic number. On the other hand, it is verified that these parameters exhibit a monotonic behaviour with the atomic number for the absolute ionization cross sections, which allows us to obtain analytical expressions for the latter.

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.

Approximate inelastic scattering cross sections of electrons

The approximate expressions for the differential inelastic scattering cross sections of electrons in a medium are proposed from distant and close interactions using generalized oscillator strength. The approximate total inelastic scattering cross section of electrons in a medium is calculated by using the presented expressions for distant and close interactions. For several media, the calculated K- and L-shell electron-impact ionization cross sections, total electron-impact ionization cross sections and inelastic mean free paths and collision stopping powers of electrons are compared to other theoretical and experimental values available from the literature.

Measurement of L-shell ionization cross sections for niobium by electron impact

L-shell ionization cross sections of Nb by electron impact in the energy range from 3 to 40 keV have been determined with an Si(Li) X-ray detector. Influence of reflected electrons from backing on the measurement was corrected using an electron transport model. The experimental results are compared with the theoretical calculations of Gryzinski (1965 Phys. Rev. A138 336) and McGuire (1977 Phys. Rev. A16 73).

Experimental evidence of threshold effects in the energy loss of protons in carbon and aluminum due to inner shell ionization

We explore the contributions of inner shell ionization to the energy loss of 7 to 270 keV protons in C and Al foils under experimental conditions such that the product of the observation angle and the projectile energy is kept constant. By normalizing these energy loss measurements to the energy loss in the forward direction we observe a pronounced rising behavior with increasing energy. This effect appears in the same range of energies where the respective K- and L-shell ionization cross sections of these elements show a similar threshold behavior. Based also on various theoretical considerations we interpret these results as clear evidence of the inner shell ionization contribution to the energy loss.

Relative Variation of K- And L-Shell Ionization Cross Sections by Electron Impact

Knowledge of inner-shell ionization cross sections by electron impact is needed for quantitative procedures in electron probe microanalysis (EPMA) and Auger electron spectroscopy (AES) The common practice is to use semi-empirical formulas, based on the asymptotic limit of the Bethe theory, which sometimes are used beyond their domain of validity. Experimental measurements of ionization cross sections are scarce and affected by considerable uncertainties, thus a mere comparison with experimental data does not permit to draw a definite conclusion abou the accuracy of the various formulas. In this communication, we present new measurements o the relative variation of K- and L-shell ionization cross sections deduced from the counting rate of characteristic x-rays emitted by extremely thin films of Cr, Ni, Cu, Te, Au and Bi bombardec by keV electrons.The studied films were produced by thermal evaporation on backing self-supported 30 nm carbon films.

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.