Supercritical instability of Dirac electrons in the field of two oppositely charged nuclei

TL;DR

This paper investigates the supercritical instability of Dirac electrons in a finite dipole potential, revealing a novel phenomenon where the electron's bound state shifts localization between nuclei, indicating spontaneous pair creation.

Contribution

It introduces a new type of supercriticality in Dirac electrons in a dipole field, considering finite nuclear size and analyzing wave function localization changes.

Findings

Critical dipole moment induces wave function localization shift.

Supercriticality leads to spontaneous electron-positron pair creation.

Wave function transitions from one nucleus to the other at criticality.

Abstract

The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the finite nuclear size. It is shown that if the dipole momentum reaches a certain critical value, the novel type of supercriticality occurs; namely, the wave function of the highest occupied electron bound state changes its localization from the negatively charged nucleus to the positively charged one. This phenomenon can be interpreted as a spontaneous creation of an electron-positron pair in vacuum, with each of the created particles being in the bound state with the corresponding nucleus and partially screening it.