Electron-Positron Pair Production in Space- or Time-Dependent Electric Fields

TL;DR

This paper derives a semiclassical formula for electron-positron pair production rates in space- and time-dependent electric fields, analyzing boundary effects and applications to atomic level filling in high-Z nuclei.

Contribution

It provides a general expression for pair production in z-dependent electric fields, including magnetic effects and boundary conditions, extending previous models.

Findings

Derived a general pair production rate formula for z-dependent fields

Analyzed boundary effects on pair production rates

Calculated atomic level filling rates for high-Z nuclei

Abstract

Treating the production of electron and positron pairs by a strong electric field from the vacuum as a quantum tunneling process we derive, in semiclassical approximation, a general expression for the pair production rate in a $z$-dependent electric field $E(z)$ pointing in the $z$-direction. We also allow for a smoothly varying magnetic field parallel to $E(z)$. The result is applied to a confined field $E(z)\not=0$ for $|z|\lesssim \ell $, a semi-confined field $E(z)\not=0$ for $ z\gtrsim 0 $, and a linearly increasing field $E(z)\sim z$. The boundary effects of the confined fields on pair-production rates are exhibited. A simple variable change in all formulas leads to results for electric fields depending on time rather than space. In addition, we discuss tunneling processes in which empty atomic bound states are spontaneously filled by negative-energy electrons from the vacuum under positron emission. In particular, we calculate the rate at which the atomic levels of a bare nucleus of finite size $r_{\rm n}$ and large $Z\gg 1$ are filled by spontaneous pair creation.