Problems of the correspondence principle for the recombination cross section in dark plasma

TL;DR

This paper examines the challenges of applying the correspondence principle to recombination cross sections in dark plasma, highlighting discrepancies between classical and quantum approaches in dark matter particle interactions.

Contribution

It identifies issues in the semiclassical description of recombination processes in dark matter models and discusses conditions for classical and quantum cross-section equivalence.

Findings

Discrepancies between classical and quantum recombination cross sections.

Conditions under which classical cross sections approximate quantum ones.

Analysis relevant to dark matter particle interactions.

Abstract

We raise the issues concerning correspondence principle in description of a recombination of oppositely charged particles. These issues have come from cosmological dark matter (DM) problem investigations. Particles possessing Coulomb-like interaction are considered. Such Coulomb-like interaction between DM particles is assumed though the problem seems to be more general. Analysis showed that usage of different semiclassical approaches leads to the apparent discrepancy between numbers of recombination acts. We attempted to find some conditions under which classical cross-section (which relates to multiple soft photon process) reduces to quantum one, which is obtained in semi-classical approximation (Kramers' formula). We just draw attention to this and provide some (not decisive) arguments.