On Quantum and Classical Treatments of Radiative Recombination

Abstract

The quantum-mechanical solution to the problem of radiative recombination of an electron in a Coulomb field, obtained in the approximation of the smallness of the electron coupling with the radiation field, has been known for a long time. However, in astrophysics, the classical approach, which does not explicitly use this smallness, is sometimes used to describe similar processes in systems of magnetic monopoles or self-interacting dark matter particles. The importance of such problems is determined by the fact that recombination processes play a crucial role in the evolution of the large-scale structure of the Universe. Therefore, of particular interest is the fact that the classical and quantum expressions for the recombination cross section differ significantly in magnitude. It is shown that the applicability of quantum and classical approaches to radiative recombination is closely related to the radiated angular momentum and its quantization. For situations where the classical approach is not suitable, a semi-classical approach based on the angular momentum quantization is proposed, in some respects an alternative to the well-known semi-classical Kramers' approach.

References in corpus (11)

• Dark Matter's secret liaisons: phenomenology of a dark U(1) sector with bound states
• Make Dark Matter Charged Again
• Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential
• Seeding Supermassive Black Holes with Self-Interacting Dark Matter: A Unified Scenario with Baryons
• Effects of Bound States on Dark Matter Annihilation
• Dark atoms and composite dark matter
• Exploring the astrophysics of dark atoms
• High Energy Positrons and Gamma Radiation from Decaying Constituents of a two-component Dark Atom Model
• Electron radiative recombination with a hydrogen-like ion
• On the classical description of the recombination of dark matter particles with a Coulomb-like interaction
• Effects of new long-range interaction: Recombination of relic Heavy neutrinos and antineutrinos