Subshell Ionization Cross Sections Research Articles

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Photoionization of C60 at high energies

Calculations of the photoionization cross section of C60 including all valence and core subshells have been carried out for photon energies up to 1 keV using density functional theory (DFT) and time-dependent DFT (TDDFT) within the framework of a fully molecular model. The high-energy valence subshell cross sections behave rather differently than the results from model potentials where the cross section falls far too rapidly with energy. This unphysical behavior of the model calculations is traced to smearing out of the carbon nuclei in the model potentials which makes it difficult for momentum to be conserved at the higher energies. Comparison with 60 times carbon atomic cross section sheds light on similarities and differences. The high energy behavior of individual valence cross sections reflects the amount of C 2s/2p mixing in the molecular orbitals.

Implementation of the EPICS2017 database for photons in Geant4

This paper describes in detail the implementation of Geant4 Livermore electromagnetic physics models based on the EPICS2017 database for the low energy transport of photons. These models describe four photon processes: gamma conversion, Compton scattering, photoelectric effect and Rayleigh scattering. New parameterizations based on EPICS2017 were performed for scattering functions of Compton effect, subshell cross-sections of the photoelectric effect and form factors of Rayleigh scattering, in order to improve the precision of fitted values compared to tabulated values. Comparisons between new and old parameterizations were also carried out to evaluate the precision of the new parameterizations. The models were tested through a comparative study, in which the mass attenuation coefficient was calculated for both total photon interaction and each process using Geant4 simulations based on EPICS2017 and EPDL97 respectively. The results obtained from the simulations were found in good agreement with the XCOM reference data.

Experimental and theoretical L -subshell ionization cross sections for 83Bi by electron impact from the L3 threshold to 100 keV

We report experimental and theoretical Bi ${L}_{1}$, ${L}_{2}$, and ${L}_{3}$ subshell ionization cross sections by the impact of electrons with energies from the Bi ${L}_{3}$ ionization threshold to 100 keV. The x-ray spectra have been acquired with two Si drift detectors placed in vacuum, which allowed us to better evaluate the peak fit procedure in the $L$ multiplet. The $L\ensuremath{\alpha}$, $L\ensuremath{\beta}$, $L\ensuremath{\gamma}$, $L\ensuremath{\ell}$, and $L\ensuremath{\eta}$ x-ray production cross sections, measured with relative uncertainties ranging from $5%$ to $9%$, and two sets of atomic relaxation parameters have been used to derive the Bi ${L}_{1}$, ${L}_{2}$, and ${L}_{3}$ ionization cross sections. Although the experimental uncertainties of the subshell ionization cross sections are smaller than those of the few previous measurements, they remain large due to the uncertainties associated with the relaxation parameters. Furthermore, ionization cross sections have been calculated for the three $L$ subshells with the subconfiguration average distorted-wave (SCADW) formalism, which includes the full two-body retarded electromagnetic interaction between the projectile and target electrons. These theoretical cross sections are $15%$ to $30%$ lower than the measured values, but the agreement is reasonable given the aforementioned high uncertainties. We have also found that the simpler distorted-wave Born approximation yields subshell ionization cross sections that match those computed with the SCADW method.

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.

Distorted wave model for sub-shell electron capture cross sections of noble gases by bare ion impact

SynopsisElectron capture from noble gases (He, Ne and Ar) are investigated in the framework of the quantum-mechanical distorted wave model. In this model, we use an independent electron model taking particular care of the representation of the bound and continuum target states. The results for partial and total capture cross sections are compared with other theoretical calculations and experimental data. The present results are found to be in very good agreement with the available experimental findings.

Low energy carbon ion induced M X-ray relative intensities for 70Yb, 82Pb and 83Bi

In the present work, the intensity ratios, IMk/IMn (exp) (k = ξ, β, γ, m1; n = αβ, α), for 70Yb, 82Pb and 83Bi induced by the Cq+ (q = 4, 5) ions having energies in the range 800–1500 keV have been measured. These intensity ratios have been compared with those calculated using the ECPSSR model based carbon ion induced Mj (j = 1–5) sub-shell ionization cross sections, the X-ray emission rates based on the Dirac-Fock (DF) model, two sets of the fluorescence and Coster-Kronig yields based on the non-relativistic Hermann-Skillman potential calculations and those based on the relativistic Dirac-Hartree-Slater model. Significant differences observed between the present measured and calculated ratios could be due to multiple-ionization induced in the investigated elements by the incident carbon ions.

N‐shell ionization cross sections by proton impact in the BEA

The N‐subshell ionizations cross sections of heavy elements by proton impact have been calculated in the binary‐encounter approximation. The momentum distribution of target electrons is taken into account by the use of the nonrelativistic and relativistic hydrogenic models and the Hartree–Fock–Roothaan and the relativistic Hartree–Fock–Roothaan methods. The obtained subshell ionization cross sections are compared with the experimental data and other theoretical calculations. The electronic relativistic effect and the wave‐function effect on N‐shell ionization cross sections are discussed.

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.

M-X-ray production cross sections of heavy elements by charged-particle impact

The M-subshell ionization cross sections of heavy elements by proton and helium-ion impact have been calculated in the binary-encounter approximation. The momentum distribution of target electrons is taken into account by the use of the nonrelativistic and relativistic hydrogenic models and the Hartree–Fock–Roothaan method. The obtained subshell ionization cross sections are converted into the M-X-ray production cross sections and compared with experimental data and other theoretical calculations. The electronic relativistic effect and the wave-function effect on M-shell ionization cross sections are studied and possible reasons for large discrepancy between theory and experiment for Mγ-X-ray production cross section are discussed.

Theory and calculation of the atomic photoeffect

Abstract The so-called elementary theory of the atomic photoeffect is presented in a form that is suited for practical numerical calculation of subshell cross sections and angular distributions of emitted photoelectrons. Atomic states are described within the independent-electron approximation, with bound and free one-electron orbitals that are solutions of the Dirac equation with the Dirac–Hartree–Fock–Slater self-consistent potential of the ground-state configuration. Detailed derivations are given of subshell cross sections for both excitation to discrete bound levels and ionization. In the case of ionization, the cross section differential in the direction of the photoelectron is obtained for partially polarized photons, with the polarization specified by means of the Stokes parameters. The theoretical formulas have been implemented in a computer program named photacs that calculates tables of excitation and ionization cross sections for any element and subshell. Numerical calculations are practicable for excitations to final states with the principal quantum number up to about 20 and for ionization by photons with energy up to about 2 MeV. Elaborate extrapolation schemes for determining the subshell cross section for excitation to bound levels with larger principal quantum numbers and for ionization by photons with higher energies are described. The effect of the finite width of atomic energy levels is accounted for by convolving the calculated subshell cross-section with a Lorentzian profile.

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.

M-shell ionization cross sections by proton impact on gold in the binary-encounter approximation

The M-subshell ionization cross sections by proton impact on gold have been calculated in the binary-encounter approximation. The momentum distribution of target electron is estimated nonrelativistically and relativistically by the use of the hydrogenic model and the Hartree–Fock method. The obtained subshell ionization cross sections are converted into the M-X-ray production cross sections and compared with experimental data and other theoretical calculations. The electronic relativistic effect and the wave-function effect on M-shell ionization cross sections are discussed.

Kinematically complete measurements for electron capture in collision of keV energy ions with atomic and molecular targets

We have performed a kinematically complete experiment to obtain sub-shell resolved differential cross sections for electron capture from inert gas targets in collisions with keV energy singly and doubly charged ions. Measurements were done for single and double capture and transfer ionization using a "reaction microscope".

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.

Photoionization of Xe insideC60: Atom-fullerene hybridization, giant cross-section enhancement, and correlation confinement resonances

A theoretical study of the subshell photoionization of the Xe atom endohedrally confined in ${\mathrm{C}}_{60}$ is presented. Powerful hybridization of the Xe $5s$ state with the bottom edge of ${\mathrm{C}}_{60} \ensuremath{\pi}$ band is found that induces strong structures in the $5s$ ionization, causing the cross section to differ significantly from earlier results that omit this hybridization. The hybridization also affects the angular distribution asymmetry parameter of Xe $5p$ ionization near the Cooper minimum. The $5p$ cross section, on the other hand, is greatly enhanced by borrowing considerable oscillator strength from the ${\mathrm{C}}_{60}$ giant plasmon resonance via the atom-fullerene dynamical interchannel coupling. Beyond the ${\mathrm{C}}_{60}$ plasmon energy range the atomic subshell cross sections display confinement-induced oscillations in which, over the large $4d$ shape resonance region, the dominant $4d$ oscillations induce their ``clones'' in all degenerate weaker channels known as correlation confinement resonances.

Characteristic plateau in theL1-subshell ionization cross section of Ag induced by proton collisions

A characteristic dependence of the proton-induced 2s subshell ionization cross section generated by the nodal structure of the 2s wave function was probed via high-resolution measurements of the Lbeta{sub 3} (L{sub 1}-M{sub 3}) and Lbeta{sub 6} (L{sub 3}-N{sub 1}) x-ray lines of Ag. The intensity ratio of the measured lines depends strongly on the proton energy exhibiting a pronounced maximum around 0.4 MeV. The experimental intensities are critically compared to the theoretically predicted values. The latter were obtained using the ionization cross sections calculated within the semiclassical approximation employing hydrogenlike and Dirac-Fock electron wave functions.

L x-ray production cross sections from 50-300 keV proton impact on selected 4d transition elements

L x-rays were measured from the impact on thick targets of protons in the 50-300 keV energy range. The derived L sub-shell cross sections were compared with the ECPSSR theory and with measurements by others. It was found that ECPSSR over-predicts the measurements as the impact energy decreases.

L sub-shell cross sections for proton impact on selected 4d transition elements

L x-rays excited from thick elemental targets of Y, Zr, Nb, Mo, Rh, Pd, Ag and Sn by proton impact in the energy range 50–300 keV were measured with a high-resolution Si(Li) detector equipped with an ultra-thin window. The L sub-shell x-ray production cross sections were determined from a thick-target analysis of the x-ray yields. These were compared with the ECPSSR theory along with various atomic parameter databases and including modifications using the united-atom (UA) binding energy correction.

Cooper-minimum-type structure in proton-inducedL1- andL3-subshell x-ray line intensities of Pd measured with high-resolution x-ray spectroscopy

We report on high-resolution measurements of the ${L}_{1}$- and ${L}_{3}$-subshell x-ray lines of Pd induced by 0.5\char21{}3.0 MeV proton bombardment. The experimental results for the relative intensities of the $L{\ensuremath{\beta}}_{3}$ $({L}_{1}\text{\ensuremath{-}}{M}_{3})$, $L{\ensuremath{\beta}}_{4}$ $({L}_{1}\text{\ensuremath{-}}{M}_{2})$, and $L{\ensuremath{\beta}}_{6}$ $({L}_{3}\text{\ensuremath{-}}{N}_{1})$ lines are compared to the theoretically predicted values employing $L$-subshell ionization cross sections calculated within the semiclassical approximation and the energy-loss Coulomb-repulsion perturbed-stationary-state relativistic theory. A structure of the ${L}_{1}$-subshell cross section at low proton energies generated by the nodal structure of the $2s$ wave function, analogous to the well-known Cooper minimum in the photoabsorption cross section, has been observed also for the case of charged particle ionization. In addition, the influence of the multiple ionization on the intensity ratio of the two most intense ${L}_{1}$-subshell x-ray transitions is studied by comparing the proton-induced intensities with the corresponding photoinduced value measured in an experiment employing monochromatic synchrotron radiation with an energy tuned just above the ${L}_{1}$ edge.