Particle scattering and vacuum instability by exponential steps

TL;DR

This paper investigates particle scattering and vacuum instability in a novel exponential peak electric field, providing exact solutions to quantum equations and analyzing particle creation and vacuum decay in various peak configurations.

Contribution

It introduces a new class of inhomogeneous electric fields with exact solutions, enabling detailed analysis of particle scattering and vacuum instability.

Findings

Derived exact solutions for Dirac and Klein-Gordon equations in exponential peak fields.

Calculated probabilities of particle scattering and vacuum decay.

Analyzed different peak configurations and regularization methods.

Abstract

Particle scattering and vacuum instability in a constant inhomogeneous electric field of particular peak configuration that consists of two (exponentially increasing and exponentially decreasing) independent parts are studied. It presents a new kind of external field where exact solutions of the Dirac and Klein-Gordon equations can be found. We obtain and analyze in- and out-solutions of the Dirac and Klein-Gordon equations in this configuration. By their help we calculate probabilities of particle scattering and characteristics of the vacuum instability. In particular, we consider in details three configurations: a smooth peak, a sharp peak, and a strongly asymmetric peak configuration. We find asymptotic expressions for total mean numbers of created particles and for vacuum-to-vacuum transition probability. We discuss a new regularization of the Klein step by the sharp peak and compare this regularization with another one given by the Sauter potential.