Particle creation by peak electric field

TL;DR

This paper analyzes particle creation in a peak electric field composed of exponential increase and decrease, deriving exact solutions to the Dirac equation and calculating key particle creation characteristics.

Contribution

It provides exact solutions and detailed analysis of particle creation in a complex peak electric field, extending previous models with new asymptotic insights.

Findings

Exact solutions to the Dirac equation in peak electric fields

Calculated differential mean numbers of created particles

Analyzed asymptotic regimes and compared with decaying fields

Abstract

The particle creation by the so-called peak electric field is considered. The latter field is a combination of two exponential parts, one exponentially increasing and another exponentially decreasing. We find exact solutions of the Dirac equation with the field under consideration with appropriate asymptotic conditions and calculate all the characteristics of particle creation effect, in particular, differential mean numbers of created particle, total number of created particles, and the probability for a vacuum to remain a vacuum. Characteristic asymptotic regimes are discussed in detail and a comparison with the pure asymptotically decaying field is considered.