Atomic Level Widths Research Articles

THEORETICAL STUDYING SPECTRAL CHARACTERISTICS OF Tm ATOM WITHIN OPTIMIZED RELATIVISTIC MANY-BODY THEORY

Theoretical studying Rydberg spectrum of complex lanthanide atom of Tm has been performed within the relativistic many-body perturbation theory and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham-Breit ones. Optimization has been fulfilled by means of introduction of the special gauge parameter to the Fock and Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital sets, generated by the corresponding zeroth approximation Hamiltonian. The calculated energies and widths of autoionization resonant states 4f--1j 6s(J12)nsnp[J] of the Tm atom with n=25-35 are presented and compared with known theoretical results, received within other approaches. Two main types of the Rydberg autoionization resonances decay, namely, the classic Beutler-Fano decay channel and a new Ivanov et al reorientation-type decay channel ar4e studied. It is noted that, for example, for autoionization resonant states with the considered values of n, the decay of resonances occurs along both channels, and it is extremely difficult to understand a priori which of them is dominant.

THEORETICAL STUDYING SPECTRAL CHARACTERISTICS OF Zn-LIKE IONS ON THE BASIS OF RELATIVISTIC MANY-BODY PERTURBATION THEORY

A theoretical study of the spectroscopic characteristics of Zn-like multiply charged ions is carried out within the framework of the relativistic many-body perturbation theory. The optimized Dirac-Kohn-Shem approximation was chosen as the zero approximation of the relativistic perturbation theory. Optimization has been fulfilled by means of introduction of the parameters to the Kohn-Sham exchange and correlation potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian.

THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

Two-photon atomic level widths at finite temperatures

The thermal two-photon level broadening of the excited energy levels in the hydrogen and H-like helium is evaluated via the imaginary part of thermal two-loop self-energy correction for bound electron. All the derivations are presented in the framework of rigorous quantum electrodynamic theory at finite temperatures and are applicable for the H-like ions. On this basis, we found a contribution to the level broadening induced by the blackbody radiation which is fundamentally different from the usual line broadening caused by the stimulated two-photon decay and the Raman scattering of thermal photons. Numerical calculations of the two-loop thermal correction to the two-photon width for the $2s$ state in hydrogen and singly ionized helium atoms show that the effect could significantly exceed the higher-order relativistic and radiative QED corrections commonly included in the calculations. In addition, the thermal two-loop self-energy correction significantly exceeds the "ordinary" stimulated one-photon depopulation rate at the relevant laboratory temperatures. In this work, detailed analysis and the corresponding comparison of the effect with the existing laboratory measurements in H-like ions are carried out.

ТЕОРЕТИЧНЕ ВИВЧЕННЯ СПЕКТРУ ІТЕРБІЮ НА ОСНОВІ РЕЛЯТИВІСТСЬКОЇ БАГАТОЧАСТКОВІ ТЕОРІЇ ЗБУРЕНЬ: ДВІЧІ ЗБУДЖЕНІ ВАЛЕНТНІ СТАНИ

Theoretical studying spectrum of doubly excited valence states of the ytterbium is carried out within the relativistic many-body perturbation theory and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian

Advanced computational approach in electron-collisional spectroscopy of atoms and multicharged ions in plasmas

An advanced computational approach to determination of the electron-collisional strengths and cross-sections for atomic ions in the Debye plasmas is presented and used to calculate effective collision strengths of the Kr26+ Ne-like ion excitation states for temperature T=5×106K and density ne==1014cm−3 . The obtained results are compared with the R-matrix data by Griffin et al and other theoretical estimates. The approach is based on the generalized relativistic energy formalism and relativistic many-body perturbation theory with the Debye shielding model Hamiltonian for electron-nuclear and electron-electron systems. The optimized one-electron representation in the perturbation theory zeroth approximation is constructed by means of the correct treating the gauge dependent multielectron contribution of the lowest perturbation theory corrections to the radiation widths of atomic levels.

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.

Influence of host matrices on krypton electron binding energies and KLL Auger transition energies

The low-energy electron spectra emitted in the radioactive decay of the 83Rb and 83Sr isotopes were measured with a combined electrostatic electron spectrometer. Radioactive sources used were prepared by ion implantation of 83Sr into a high purity polycrystalline platinum foil at 30keV and by vacuum-evaporation deposition of 83Rb on the same type of foil. From the measured conversion electron spectra, the electron binding energies (referenced to the Fermi level) for the K, L1, L2, L3, M1, M2, and M3 shell/subshells of krypton in the platinum host were determined to be 14316.4(12), 1914.3(9), 1720.3(9), 1667.6(9), 281.5(9), 209.6(13), and 201.2(15)eV, respectively, and those for the evaporated layer were observed to be lower by 0.7(1)eV. For both host matrices, values of 2.3(2), 4.6(2), 1.7(2), 1.3(2), and 3.2(3)eV were obtained for the krypton K, L1, L2, L3, and M1 natural atomic level widths, respectively. The absolute energies of 10838.5(9) and 10839.5(10)eV were measured for the KL2L3(1D2) Auger transition in krypton implanted in Pt and generated in the evaporated rubidium layer, respectively. A value of 601.0(8)eV was measured for the energy difference of the KL2L3(1D2) transitions in Rb and Kr in the Pt host. Multiconfiguration Dirac–Fock calculations of the krypton KLL transition energies and intensities were also performed.

Improved energies for the 5.2 keV M1 and 42.0 keV M2 nuclear transitions in 83Rb

The low-energy electron spectrum following the decay of 83Sr was analysed at high instrumental resolution by an electrostatic spectrometer. Significantly improved energies of \( 5235.7\pm 0.8\) and \( 42078.0\pm 1.8\) eV were determined from the conversion electron spectra for the nuclear transitions depopulating the first 3/2- and the second \( 9/2^{+}\) excited states in 83Rb to the \( 5/2^{-}\) ground state, respectively. The M1 character for the 5.2keV nuclear transition was confirmed and the E2 admixture parameter \( \delta^{2}(E2/M1)=(2.6\pm 0.2)\times 10^{-5}\) was obtained. Values of \( 2.8\pm 0.2\), \( 3.8\pm 0.2\), \( 1.4\pm 0.3\), \( 1.4\pm 0.4\), and \( 4.1\pm 0.3\) eV were determined for the K, L1, L2, L3, and M1 natural atomic level widths of rubidium, respectively.

The xraylib library for X-ray–matter interactions. Recent developments

This work presents the recent developments of xraylib, an ANSI C library that provides convenient access to a large number of X-ray related databases, with a focus on quantitative X-ray fluorescence applications. The enhancements include improved X-ray fluorescence production cross sections that take into account cascade effects and M-lines, as well as revised line energies, atomic level widths, Compton broadening profiles etc. A full overview of the complete application programming interface is presented.

${\boldsymbol N}\boldsymbol{\bar N}$ exotics and antiprotonic atoms

The BES Collaboration measurements of J/ψ radiative decays into \( p{\bar p}\) indicate a strong enhancement at \( p {\bar p}\) threshold. In a related experiment a peak in the invariant π + π − η′ mass is observed. It is shown that both structures may be related to a broad \( N{\bar N}\) quasi-bound state in the \(^{11}S_{0} \) wave. The existence of this state finds additional support from the antiprotonic atom level widths. It is also explained by a traditional model of \( N \bar{N} \) interactions based on G-parity transformation. The level widths in H, D and He antiprotonic atoms and the radiochemical studies of \( {\bar p}\) capture in nuclei indicate the existence of another near-threshold quasi-bound state in a P wave.

ON THE SCATTERING LENGTH OF THE K-d SYSTEM

Multiple-scattering approximations to Faddeev calculations of the K-d scattering length are reviewed and compared with published [Formula: see text] fully reactive Faddeev calculations. A new multiple-scattering approximation which goes beyond the 'fixed-center' assumption for the nucleons is proposed, aiming at accuracies of 5–10%. A precise value of the K-d scattering length from the measurement of the K-d 1s atomic level shift and width, planned by the DEAR/SIDDHARTA collaboration, plus a precise value for the K-p scattering length by improving the K-p atom measurements, are essential for extracting the K-n scattering length, for resolving persistent puzzles in low-energy [Formula: see text] phenomenology and for extrapolating into [Formula: see text]-nuclear systems.

The effective operator for atomic level widths due to l1N1l2N2→l1N1+1l2N2−2εl3 Auger transitions

The effective operator AΓ for the Auger l1N1 l2N2→ l1N1+1 l2N2- 2εl3 transitions was determined in the nonrelativistic approximation in the second quantization representation in the case of normal ordering of electron creation and annihilation operators. The matrix element of AΓ yields a partial Auger width of a level. The specific transitions when l2=1, 2 and l1> 0 were considered in detail. The general formula for a matrix element of AΓ was derived when a wavefunction with open-shells was presented in normal coupling. Compact expressions for the matrix elements of AΓ in the case l1N1 l22 when N1=1, 2, 4l1+1 and 4l1 were obtained. The selection rules for matrix elements of AΓ are discussed by using the quasispin technique.

Formula omitted]–nuclear bound states in a dynamical model

A comprehensive data base of K − –atom level shifts and widths is re-analyzed in order to study the density dependence of the K ¯ –nuclear optical potential. Significant departure from a t eff ρ form is found only for ρ ( r ) / ρ 0 ≲ 0.2 and extrapolation to nuclear-matter density ρ 0 yields an attractive potential, about 170 MeV deep. Partial restoration of chiral symmetry compatible with pionic atoms and low-energy pion–nuclear data plays no role at the relevant low-density regime, but this effect is not ruled out at densities of order ρ 0 and beyond. K ¯ –nuclear bound states are generated across the periodic table self consistently, using a relativistic mean-field model Lagrangian which couples the K ¯ to the scalar and vector meson fields mediating the nuclear interactions. The reduced phase space available for K ¯ absorption from these bound states is taken into account by adding an energy-dependent imaginary term which underlies the corresponding K ¯ –nuclear level widths, with a strength required by fits to the atomic data. Substantial polarization of the core nucleus is found for light nuclei, and the binding energies and widths calculated in this dynamical model differ appreciably from those calculated for a static nucleus. A wide range of binding energies is spanned by varying the K ¯ couplings to the meson fields. Our calculations provide a lower limit of Γ K ¯ = 50 ± 10 MeV on the width of nuclear bound states for K ¯ -binding energy in the range B K ¯ ∼ 100 – 200 MeV . Comments are made on the interpretation of the FINUDA experiment at DAΦNE which claimed evidence for deeply bound K − p p states in light nuclei.

Evaluation of the energy‐dispersive x‐ray spectra of high‐Z elements using Gaussian and Voigt peak shape profiles

AbstractThe AXIL computer program, aimed at x‐ray spectral deconvolution, was extended in order to take into account the broadening of peaks of K‐series radiation of high‐Z elements (Z > 50) due to the increasing contribution of the natural linewidth to the peak width. This effect needs to be taken into account in energy‐dispersive spectrometry of K‐series radiation of heavy elements, such as W, Au, Pb and U. The so‐called Voigt peak profile function was implemented into the AXIL computer code. Based on the published literature data, a library of natural atomic level widths was created, containing the data for K, L1, L2, L3 atomic level widths of elements up to Z = 94. The database was necessary to calculate the Voigt peak profiles. The AXIL program user interface and the fitting procedures were adapted, allowing us to perform spectral evaluation using either Gaussian or Voigt peak profiles. The relevance of fitting the x‐ray spectra of K‐series radiation of high‐Z elements with the Voigt peak shape model versus Gaussian peak approximation was thoroughly examined with the aid of simulated and measured spectra. The experimental x‐ray spectra were measured using a high‐voltage x‐ray tube spectrometer utilizing a 130 kV/65 W tungsten anode x‐ray tube and an ultra‐low energy germanium detector. The results obtained showed that when using the Gaussian peak model the calculated peak areas and fitted peak widths are systematically biased. It was found that the value of the systematic error is a linear function of the ratio of the natural linewidth to the spectrometer energy resolution at the peak position. Copyright © 2001 John Wiley & Sons, Ltd.

πΛΣcoupling extracted from hyperonic atoms

The latest measurements of the atomic level width in $\ensuremath{\Sigma}$-hyperonic Pb atoms offer the most accurate datum in the region of low-energy $\ensuremath{\Sigma}$-hyperon physics. Atomic widths are due to the $\ensuremath{\Sigma}N$-$\ensuremath{\Lambda}N$ conversion which in high-angular-momentum states is dominated by one-pion exchange. A joint analysis of the ${\ensuremath{\Sigma}}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\Lambda}n$ scattering data and atomic widths allows us to extract the pion-hyperon coupling constant ${f}_{\ensuremath{\pi}\ensuremath{\Lambda}\ensuremath{\Sigma}}^{2}/4\ensuremath{\pi}=0.048\ifmmode\pm\else\textpm\fi{}0.005$ (stat) $\ifmmode\pm\else\textpm\fi{}0.004$ (syst) or ${G}_{\ensuremath{\pi}\ensuremath{\Lambda}\ensuremath{\Sigma}}^{2}=13.3\ifmmode\pm\else\textpm\fi{}1.4$ (stat) $\ifmmode\pm\else\textpm\fi{}1.1$ (syst).

WIDTHS OF THE ATOMIC K–N7 LEVELS

Atomic level widths obtained from experimental measurements are collected in Table I, along with the corresponding theoretical widths derived from the Evaluated Atomic Data Library (EADL) of Lawrence Livermore National Laboratory; these EADL values are based upon the Dirac–Hartree–Slater version of the independent-particle model. In a minority of cases, many-body theory predictions are also provided. A brief discussion of the manner in which the experimental widths were deduced from spectroscopic data is included. The bulk of the data are for elements in the solid state, but a few data for gases and simple compounds are included.For the K, L2, L3, and M5 levels, where Coster–Kronig contributions do not contribute or contribute only to a small extent to the overall widths, the EADL predictions appear satisfactory for elements in the solid state. For other levels, where Coster–Kronig and super-Coster–Kronig transitions have large probabilities within the independent-particle model, this model is not satisfactory. Table II provides a complete set of recommended elemental values based upon consideration of the available experimental data.

K− and [formula omitted] deeply bound atomic states

The strongly absorptive optical potentials V opt which have been deduced from the strong-interaction level shifts and widths in X-ray spectra of K − and p ̄ atoms produce effective repulsion leading to substantial suppression of the atomic wave functions within the nucleus. The width of atomic levels then saturates as function of the strength of Im V opt. We find that `deeply bound' atomic states, which are inaccessible in the atomic cascade process, are generally narrow, due to this mechanism, over the entire periodic table and should be reasonably well resolved. These predictions are insensitive to V opt, provided it was fitted to the observed X-ray spectra. In contrast, the nuclear states bound by V opt are very broad and their spectrum depends sensitively on details of V opt. We discuss production reactions for K − atomic states using slow K − mesons from the decay of the φ(1020) vector meson, and the ( p ̄ ,p ) reaction for p ̄ atomic states. Rough cross section estimates are given.

Recent developements in charge-transfer theory

In this paper we discuss some recent theoretical developments of importance in the area of charge transfer between atoms and surfaces. Using the complex scaling method we have calculated the energy shift and broadening of atomic levels near metal surfaces. Two novel applications will be discussed. The first concerns the interaction of atomic Rydberg levels with clean metal surfaces. It is shown that as Rydberg atoms approach a surface, strong hybridization occurs that depends sensitively on both the atom-surface separation and the details of the surface potential. The widths of the hybridized states can differ by several orders of magnitude depending on their orientation with respect to the surface. The second application is an investigation of how dielectric overlayers adsorbed on metal surfaces can influence the energy shift and broadening of atomic levels. The calculations show that the energies and widths of atomic levels near metal surfaces can be influenced strongly by thin dielectric films adsorbed on the surface.

Atomic level widths for x‐ray spectrometry

AbstractA self‐consistent set of level widths for the K–N7 subshells is assembled using literature experimental data from a variety of spectroscopic methods. In cases where Coster–Kronig processes contribute significantly, the widths differ from the predictions of the atomic single‐particle model; in the restricted regions where atomic many‐body predictions are available, the agreement is much better. The assembled widths will be useful to Si(Li) spectroscopists who wish to include natural width in the description of spectrometer lineshape; such inclusion will improve accuracy in both fundamental and analytical work. The present database is also of value in identifying where improvements to the currently incomplete knowledge of natural widths are most critical.