Cross Sections for Inelastic Scattering of Electrons by Atoms - Selected Topics Related to Electron Microscopy

We begin with a resume of the Bethe theory, which provides a general framework for discussing the inelastic scattering of fast electrons and leads to powerful criteria for judging the reliability of cross-section data. The central notion of the theory is the generalized oscillator strength as a function of both the energy transfer and the momentum transfer, and is the only non-trivial factor in the inelastic-scattering cross section. Although the Bethe theory was initially conceived for free atoms, its basic ideas apply to solids, with suitable generalizations; in this respect, the notion of the dielectric response function is the most fundamental. Topics selected for discussion include the generalized oscillator strengths for the K-shell and L-shell ionization for all atoms with Z ≤ 30, evaluated by use of the Hartree-Slater potential. As a function of the energy transfer, the generalized oscillator strength most often shows a non-monotonic structure near the K-shell and L-shell thresholds, which has been interpreted as manifestations of electron-wave propagation through atomic fields. For molecules and solids, there are additional structures due to the scattering of ejected electrons by the fields of other atoms

Photoelectron angular distribution of the excited 2p^2 3p ^2S state of atomic nitrogen

Relevant data is available at: http://www.astronomy.ohio-state.edu/~nahar/nahar_radiativeatomicdata/index.htmlCalculations of the photoelectron angular distribution asymmetry parameter ß for the excited 2p^2 3p ^2S state of atomic nitrogen have been performed using Hartree-Fock discrete and continuum wave functions with relaxation. The results show reasonably good agreement with a recent measurement of ß at a single energy.The work was supported by the U.S. Army Research Office and the National Science Foundation

Photoionization of the 7d excited state of cesium

Relevant data is available at: http://www.astronomy.ohio-state.edu/~nahar/nahar_radiativeatomicdata/index.htmlThe photoionization cross section for the excited 7d state of atomic cesium has been calculated in the Hartree-Fock approximation. The results show excellent agreement with a recent measurement.This work was supported by the U.S. Army Research Office and the National Science Foundation

Photoelectron angular distributions: energy dependence for \u3ci\u3es\u3c/i\u3e subshells

An overview of the theory of photoelectron angular distributions for atoms is presented. Its features, which are embodied in a single asymmetry parameter β in the electric dipole approximation, are examined within the framework of the angular momentum transfer formulation. The β parameter is in principle always energy dependent. Within the LS coupling approximation, however, there are instances, each representing a multitude of particular photoionization processes, in which β is an analytically determined constant. The energy dependence of the β parameters in such instances is due entirely to spin-orbit and other relativistic interactions. The study of the energy dependence of the β parameter in these cases is thus of interest because it spotlights weak-interaction effects which are usually overwhelmed by stronger interactions. We illustrate the general predictions by a detailed consideration of the energy dependence of the β parameter for s-subshell photoionization processes. It is shown that the asymmetry parameters for atomic s subshells are particularly suitable for distinguishing between purely geometrical effects on the photoelectron angular distribution, resulting from physical conservation laws, and dynamical effects arising from relativistic interactions and electron exchange and correlation. In general, the β parameters for s subshells vary with energy; such variation is largest near minima in the cross sections for the corresponding photoelectron channels and in the vicinity of resonances. However, a number of atomic photoionization transitions are identified for which β would be a constant (equal to one of the three values 2, 1/5, or - 1) were it not for relativistic interactions and (in some cases) final-state interchannel coupling and/or initial-state electron correlations. Measurement or calculation of the β parameters for such transitions thus provides a sensitive measure of the strength of relativistic interactions as well as of electron correlations

Photoelectron Angular Distributions as a Probe of Anisotropic Electron-Ion Interactions

Expressions are given for atomic photoelectron angular distributions in LS coupling in which the role of anisotropic final state electron-ion interactions emerges explicitly. Calculations of photoelectron angular distributions for atomic sulfur are presented in which these anisotropic interactions produce clear deviations from the predictions of the Cooper-Zare model. Such effects are expected to be a general feature of photoelectron angular distributions for most open-shell atoms

Relativistic calculations of angular dependent photoemission time delay

Angular dependence of photoemission time delay for the valence $np_{3/2}$ and $np_{1/2}$ subshells of Ar, Kr and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold