Lepton Number vs Coulomb Super-Criticality

Abstract

The non-perturbative effects of QED-vacuum reconstruction under influence of a supercritical EM-source ($Z>Z_{cr,1}$) are considered in view of lepton number conservation. The question is here that if the vacuum shells formation and spontaneous positron emission, associated with discrete levels diving into the lower continuum, exist in reality, then it by no means should be a signal of new physics. The reason is that the emitted positrons carry away the lepton number equal to $(-1)\times$their total number, and so the corresponding amount of positive lepton number should be shared by VP-density, concentrated in vacuum shells. In this case instead of integer lepton number of real particles there should appear the lepton number VP-density. Otherwise either the lepton number conservation in such processes must be broken, or the spontaneous positron emission prohibited. The conditions, under which the emission of vacuum positrons can be unambiguously detected on the nuclear conversion pairs background, are also discussed.