Impenetrable barriers for positrons in neighbourhood of superheavy nuclei with $Z>118$

TL;DR

This paper discovers an impenetrable potential barrier for positrons near superheavy nuclei with Z>118, which influences positron trapping and annihilation processes, especially around nuclei with Z near 170.

Contribution

It introduces a novel impenetrable barrier in quantum mechanics for positrons near superheavy nuclei, affecting positron behavior and annihilation phenomena.

Findings

Impenetrable barrier radius equals half the classical radius for stationary particles.

Barrier radius decreases as particle energy increases.

Presence of barriers leads to positron traps and a source of annihilation quanta near superheavy nuclei.

Abstract

Analysis of quantum mechanical motion of charged half-spin particles in the repulsive Coulomb field by means of second-order equation results in that an impenetrable potential barrier not explored earlier was found. For a particle at rest with a reduced mass $m$, the barrier radius is equal to half classical radius: the barrier radius decreases with increase in the particle energy. For the stable and quasi-stable nuclei with $Z>118$, presence of an impenetrable barrier as $\beta^{+}$-decay leads to the existence of "traps" for positrons in the neighbourhood of nuclei and as $Z_{cr}\simeq170$ (with emission of electron-positron pairs by vacuum) leads to the existence of a quasi-constant source of annihilation quanta.