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

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.