Pair creation by a photon in an electric field

TL;DR

This paper investigates the probability of photon-induced pair creation in a constant electric field, deriving new approximations for different energy regimes and comparing the process to magnetic field scenarios.

Contribution

It introduces a new approximation for pair creation probability at low photon energies and compares it with the magnetic field case, extending understanding of the process across energy ranges.

Findings

Probability exceeds that in magnetic fields at low energies.

Standard quasiclassical approximation is valid at high energies.

New low-energy approximation describes soft photon absorption.

Abstract

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than "vacuum" energy in electric field: $\omega\gg eE/m$. For smaller photon energies the low energy approximation is developed. At $\omega\ll eE/m$ the found probability describes the absorption of soft photon by the particles created by an electric field.