Asymptotic behavior of photoionization cross section in a central field

TL;DR

This paper analyzes the high-energy asymptotic behavior of photoionization cross sections in central fields, linking it to the Fourier transform of the potential and its analytical properties.

Contribution

It establishes a relationship between the asymptotic photoionization cross section and the Fourier transform of the potential, highlighting how singularities affect energy dependence.

Findings

Cross sections decay similarly for Coulomb-like potentials.

Power-law decay occurs for potentials with real-axis singularities.

Exponential decay occurs for potentials with complex-plane singularities.

Abstract

We demonstrate that the high energy nonrelativistic asymptotic for the photoionization cross section in a central field $V(r)$ can be expressed in terms of the asymptotic of the Fourier transform $V(p)$ of the field. We show that the cross sections drop in the same way for the fields with the Coulomb short distance behavior. The character of the cross sections energy behavior is related to the analytical properties of the function $V(r)$. The cross sections exhibit power drop for the potentials which have singularities an the real axis. They suffer the exponential drop if $V(r)$ has singularities in the complex plane.