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

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.

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