Resonant threshold two-photon $e^-e^+$ pair production onto the lowest Landau levels in a strong magnetic field

TL;DR

This paper investigates electron-positron pair production by two photons in a strong magnetic field, focusing on resonance conditions and calculating the cross-section for lowest Landau levels, advancing understanding of quantum processes in extreme magnetic environments.

Contribution

It provides a detailed analysis of the resonance conditions and estimates the cross-section for pair production at the lowest Landau levels in strong magnetic fields, which was not previously thoroughly explored.

Findings

Resonance conditions for pair production are established.

Resonant cross-section for lowest Landau levels is estimated.

Probability amplitude for arbitrary polarizations is derived.

Abstract

The process of electron-positron pair production by two photons in a strong magnetic field has been studied. The process kinematics is considered, and the probability amplitude for arbitrary polarizations of particles is found. The resonance conditions are established, and the resonant cross-section is estimated in the case where the electron and the positron occupy the lowest levels ($l_{e} = 1$, $l_{p} = 0$) that satisfy these resonance conditions.