Photoionization of the bound systems at high energies

TL;DR

This paper derives high-energy asymptotics for photoionization cross sections of bound systems using potential Fourier transforms, revealing model dependence in fullerenes and universal correction factors.

Contribution

It introduces a method to obtain high-energy asymptotics without solving wave equations, linking asymptotics to potential properties and analyzing model dependence.

Findings

Asymptotics expressed via Fourier transform of potential

Universal correction factor for leading asymptotics

Model dependence affects energy scale of asymptotic behavior

Abstract

We consider photoionization of a system bound by the central potential $V(r)$. We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann--Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential $V(r)$. We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model dependent. We demonstrate that if the fullerene field $V(r)$ is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which as so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster drop of the cross sections becomes important in these cases.