Resonances in positron scattering on a supercritical nucleus and spontaneous production of $e^{+}e^{-}$ pairs

TL;DR

This paper investigates resonances in positron scattering on supercritical nuclei, analyzing phase shifts and spontaneous electron-positron pair production, providing exact formulas and clarifying the physical interpretation of these phenomena.

Contribution

It offers new exact and approximate formulas for scattering phase shifts and extends analysis to positron solutions, enhancing understanding of supercritical nucleus interactions.

Findings

Confirmed resonant behavior of phase shifts

Solved Dirac equation for positrons in supercritical fields

Clarified interpretation of resonance phenomena

Abstract

We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase $\delta_{\varkappa}$ and its dependence on the energy $\varepsilon$ of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential $Z\alpha/r$ is rounded to the constant $Z\alpha/R$ for $r < R$. We confirm the resonant behavior of $\delta_{\varkappa}$ that we investigate in details. In addition to solving the Dirac equation for an electron, we solve it for a positron, in the field of the same nucleus. This clarifies the interpretation of the resonances. Our results are compared with claims made in previous works.