Magnetic vacuum polarization effects in the supercritical QED: spontaneous generation of a stable highly magnetized phase of the vacuum state

Abstract

The spontaneous generation of axial vacuum current and corresponding magnetic field with multipole structure, caused by the supercritical Coulomb source with charge $Z$ and size $R$, is explored in essentially non-perturbative approach with emphasis on the vacuum energy ${\mathcal{E}}_{\mathcal{V}\mathcal{P}}$, considered as a function of $R$ with fixed $Z$. The properties of such highly magnetized vacuum phase are studied in detail. It is shown that the arising this way magnetic component of the supercritical vacuum polarization leads to a significant decrease of the total energy of the system, which could provide the formation of a stable extra-heavy nuclear cluster. Numerical calculations proving the latter in case of the specific spherically symmetric Coulomb source with $Z=828$ are presented.