Super-critical QED-effects via VP-energy

Abstract

The properties of the QED-vacuum energy $\hbox{$\cal E $}_{VP}$ under Coulomb super-criticality condition $Z>Z_{cr,1}$ are explored in essentially non-perturbative approach. It is shown that in the supercritical region $\hbox{$\cal E $}_{VP}$ is the decreasing function of the Coulomb source parameters, resulting in decay into the negative range as $\sim -Z^4/R$. The conditions, under which the emission of vacuum positrons can be unambiguously detected on the nuclear conversion pairs background, are also discussed. In particular, for a super-critical dummy nucleus with charge $Z$ and $R(Z)\simeq 1.2(2.5Z{)}^{1/3}$ fm the lowest $1s$-level dives into the lower continuum at $Z_{cr,1}\simeq 170$ (the model of uniformly charged ball) or $Z_{cr,1}\simeq 173$ (the spherical shell model), whereupon there appears the vacuum shell with the induced charge (-$2|e|$) and the QED-vacuum becomes charged, but in both cases the actual threshold for reliable spontaneous positrons detection is not less than $Z^{\ast }\simeq 210$.

arXiv admin note: text overlap with arXiv:2201.04829