Superradiation in scattering of a Dirac particle off a point-like nucleus with Z>137 with Z>137

TL;DR

This paper extends quantum mechanics methods to analyze a Dirac particle near a supercritical nucleus with Z>137, revealing superradiation that inhibits pair creation.

Contribution

It introduces an analytical approach to singular Dirac problems for Z>137 nuclei, identifying superradiation as a new phenomenon.

Findings

Superradiation suppresses electron-positron pair creation.

Analytical solutions for Dirac equation with Z>137 are obtained.

Reflection and transmission coefficients are explicitly calculated.

Abstract

The main concepts of the recently developed approach to singular problems of quantum mechanics are extended to the Dirac particle in the Coulomb field of a point-like nucleus with its charge Z>137. The reflection and transmission coefficients, which describe, respectively, the reflection of electron by the singularity and its falling onto it, are analytically calculated, using the exact solutions of the Dirac equation. The superradiation phenomenon is found. It suppresses the widely discussed effect of spontaneous electron- positron pair creation.