Electron-Positron Vacuum Instability in Strong Electric Fields. Relativistic Semiclassical Approach

Dmitry N Voskresensky

doi:10.3390/universe7040104

Abstract

The instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at Z>137/2 for a spinless boson and at Z>137 for electron. Subsequently, focus is concentrated on description of deep electron levels and spontaneous positron production in the field of a finite-size nucleus with the charge Z>Zcr≃170. Next, these effects are studied in application to the low-energy heavy-ion collisions. Subsequently, we consider phenomenon of “electron condensation” on levels of upper continuum crossed the boundary of the lower continuum ϵ=−m in the field of a supercharged nucleus with Z≫Zcr. Finally, attention is focused on many-particle problems of polarization of the quantum electrodynamics (QED) vacuum and electron condensation at ultra-short distances from a source of charge. We argue for a principal difference of cases, when the size of the source is larger than the pole size rpole, at which the dielectric permittivity of the vacuum reaches zero and smaller rpole. Some arguments are presented in favor of the logical consistency of QED. All of the problems are considered within the same relativistic semiclassical approach.

Highlights

I dedicate this review to the blessed memory of Vladimir Stepanovich Popov, who recently left us as the result of a many-year hard illness, which prevented him working actively in his last years
Attention is focused on many-particle problems of polarization of the quantum electrodynamics (QED) vacuum and electron condensation at ultra-short distances from a source of charge
The process of the spontaneous production of positrons can be described in adiabatic approximation, since, as we have argued, we may use that (R(t)) and, since 1/Γ( (R(t))) τcol ∼> 2Rcr/vA

Summary

Introduction

I dedicate this review to the blessed memory of Vladimir Stepanovich Popov, who recently left us as the result of a many-year hard illness, which prevented him working actively in his last years. The problem of the electron-positron pair production when the ground-state electron level dives below the energy −mc (m is the electron mass, c is the speed of light) was of his interest starting from the end of 1960-th. He contributed to this problem during the 1970s. Pomeranchuk Prize in 2019 for his outstanding contributions to the theory of ionization of atoms and ions in the field of intense laser radiation and the theory of the creation of electron-positron pairs in the presence of superstrong external fields

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