Optimal supercritical potentials for the electron-positron pair-creation rate

Abstract

We examine the steady-state electron-positron pair-creation rate for supercritical electric potentials with arbitrary spatial dependence. The numerical optimization algorithms predict that the set of external fields that can maximize the production rate for positrons with a given energy take nontrivial spatial shapes. We explain the underlying physical mechanisms based on a simple analytical model that exploits resonances among the negative energy eigenstates of the Dirac Hamiltonian. The results are rather encouraging from an experimental perspective as they suggest that one does not require unachievable infinitely large fields to maximize the possible pair-creation yield. In fact, in many cases smaller electric fields lead surprisingly to larger yields for given energy ranges.