Quantum theory of the effect of post-collision interaction on the absorption of X-ray photons by a deep atomic shell

Abstract

A fundamental problem for modern atomic physics, the theoretical description of the many-particle effects of post-collision interactions in the photoionization of deep atomic shells outside the framework of quantum-mechanical perturbation theory is considered. The analytical solution of the stationary many-particle Schrödinger equation for the non-relativistic wavefunction of the system of interacting continuous spectra of atomic states is obtained using a class of weight-functions of Cauchy–Lorentz type. States considered are those resulting from: (i) direct photoionization of a deep shell of a free atom and (ii) Auger-decay of a deep vacancy with two (photo- and Auger-) electrons in the continuous spectrum. The solution takes into account: (a) the rearrangement of the continuum photoelectron wavefunction in the changing field of the atomic residue, and (b) the electrostatic interaction of photo- and Auger-electrons resulting from the Auger-decay of the vacancy. The corresponding analytical structure of the photoionization cross section of the deep atomic shell is derived. A generalization is proposed for: (a) two or more channels of Auger-decay of the deep vacancy, and (b) direct photoexcitation of the deep atomic shell.