Exact Pair Production Rate for a Smooth Potential Step

TL;DR

This paper derives an exact formula for the rate of scalar particle pair production in a smooth tanh-shaped potential, extending known results for sharp steps and uniform fields.

Contribution

It provides the first exact calculation of pair production rate for a smooth tanh potential in three dimensions, bridging gaps between idealized models.

Findings

Exact pair production rate for tanh potential derived

Results recover known limits for sharp step and uniform field

Provides a comprehensive understanding of pair production in smooth potentials

Abstract

We derive the exact rate of pair production of oppositely charged scalar particles by a smooth potential proportional to tanh kz in three dimensions. As a check we recover from this the known results for an infinitely sharp step as well as for a uniform electric field.