Particle production at a finite potential step: Transition from Euler-Heisenberg to Klein paradox

TL;DR

This paper investigates spontaneous particle pair production in a finite potential step, analyzing the transition from the Euler-Heisenberg regime to the Klein paradox, and highlights differences between spin-0 and spin-1/2 particles.

Contribution

It provides exact finite results for pair production in a $ anh$-Sauter potential step, including the sharp-edge Klein paradox limit and the conditions for spin-specific pair production.

Findings

Spin-0 particle production can surpass spin-1/2 at vacuum instability.

Exact results for pair production in the Klein paradox limit.

Smooth potential walls are necessary for spin-0 pair production in a well.

Abstract

Spontaneous pair production for spin-$1/2$ and spin-$0$ particles is explored in a quantitative manner for a static $\tanh$-Sauter potential step (SS), evaluating the imaginary part of the effective action. We provide finite-valued per unit-surface results, including the exact sharp-edge Klein paradox (KP) limit, which is the upper bound to pair production. At the vacuum instability threshold the spin-$0$ particle production can surpass that for the spin-$1/2$ rate. Presenting the effect of two opposite sign Sauter potential steps creating a well we show that spin-$0$ pair production, contrary to the case of spin-$1/2$, requires a smoothly sloped wall.