Nuclear recoil and vacuum-polarization effects on the binding energies of supercritical H-like ions

TL;DR

This paper investigates how nuclear recoil and vacuum polarization affect the energy levels of supercritical hydrogen-like ions with atomic number Z > 137, revealing that a point nucleus can effectively have Z > 137 due to these effects.

Contribution

It demonstrates that including nuclear recoil and vacuum polarization in the Dirac Hamiltonian regularizes the model and allows for energy levels to reach the negative continuum at Z > 137.

Findings

Ground state reaches negative energy continuum at Zcr = 145 without Uehling potential.

Including Uehling potential lowers Zcr to 144.

Point-like nucleus can effectively have charge Z > 137.

Abstract

The Dirac Hamiltonian including nuclear recoil and vacuum-polarization operators is considered in a supercritical regime Z > 137. It is found that the nuclear recoil operator derived within the Breit approximation regularizes the Hamiltonian for the point-nucleus model and allows the ground state level to go continuously down and reach the negative energy continuum at a critical value Zcr = 145. If the Hamiltonian contains both the recoil operator and the Uehling potential, the 1s level reaches the negative energy continuum at Zcr = 144. The corresponding calculations for the excited states have been also performed. This study shows that, in contrast to previous investigations, a point-like nucleus can have effectively the charge Z > 137.