On the resonances near the continua boundaries of the Dirac equation with a short-range interaction

TL;DR

This paper investigates resonances near the Dirac continuum boundaries using a spherical well model, concluding such resonances do not indicate spontaneous electron-positron pair production in supercritical fields.

Contribution

It demonstrates that resonant scattering near Dirac continuum edges is not evidence of pair production, challenging previous interpretations in supercritical quantum electrodynamics.

Findings

Resonances near Dirac continuum boundaries do not imply pair production.

Spherical well model effectively illustrates resonance behavior.

Resonant scattering cannot be used as a signature of supercriticality.

Abstract

Using the model of a deep spherically symmetric rectangular well as an example, it is shown that resonant scattering near the boundaries of the lower or upper Dirac continua cannot serve as evidence in favor of spontaneous electron-positron pair production in a supercritical domain.