Theoretical study of inner-shell photoionization cross sections and angular distributions

Abstract

Atomic photoionization cross sections and asymmetry parameters are calculated using a simple oneelectron model potential consisting of the positive nuclear charge at the origin surrounded by a series of negatively charged spherical shells. The radial Schrodinger equation is solved exactly for unbound states of the potential using Whittaker functions. Parameters for the model potential (shell radii and charges) are fitted using SCF charge densities. Applications are made to inner-shell ionizations of atoms and molecules as observed in ESCA (Mg K a and A1 K a photon energies), with emphasis on 1s ionizations for boron through neon and 2s and 2p ionizations for aluminum through argon. The periodic variation in cross section for ionization of a given orbital is discussed in terms of the photoelectron kinetic energy. Effects due to core relaxation are considered for the neon atom. The calculations are compared with experimental X-ray absorption coefficients and photoelectron spectral intensities.hotoelectron spectroscopy using soft X-ray sources P has recently become a widely used experimental technique for studying atoms, molecules, and solids. The basic experiment consists of bombarding a sample to be studied with nearly monoenergetic photons and measuring the properties of the ejected photoelectrons. Although most of the emphasis has centered around the energetics of the photoionization process leading to a determination of electron binding energies, with recent advances in the experimental technique it has become feasible to determine the intensity3 of photoelectron peaks as well as the angular (spatial) distri-bution4l5 of the ejected photoelectrons. With these additional parameters the experimentalist can begin to unravel more complex photoelectron spectra.6 The in-( I ) (a)

Energy dependence of the titanium, chromium, and manganese 3p photoionization cross sections using synchrotron radiation

“…Because the results for the monoxide and sesquioxide are the same within experimental error, it can be assumed that their electron-loss processes are very similar. Chapman and Lohr (30) have predicted that the cross section should increase with increasing binding energy (higher oxidation states). The observed variation, however, is too small to assign to differences in the oxidation state of the ion.…”

Computational Study of Pattern Formation for Chemically Amplified Resists in Extreme Ultraviolet Lithography

“…(1). The angular distribution of the emitted photoelectron is calculated by the following equation [16]:…”

Hybrid orbitals and the runge–lenz vector

“…This field has been used by McGuire [19] and by Chapman and Lohr [20] in calculating continuum wave-functions and photoionization cross sections. Since the field is Coulombic in each region of space, hydrogenic wave-functions matched at each shell radius form exact solutions of the Schrodinger equation.…”

“…The term in T involving,radial * While [A,, TI contains fourth derivatives with respect to Cartesian coordinates, it is easily shown to contain no derivatives higher than the third with respect to the radial coordinate r. As described in [20], not only are the piecewise Coulombic wave-functions and their first derivatives with respect to r continuous at the shell radii, but also their second derivatives are continuous. The jump discontinuities in the third radial derivatives at the shell radii are finite, so that a Dirac 6 function does not appear until fourth radial derivatives are taken.…”