Eur. Phys. J. D (2016) 70: 18
https://doi.org/10.1140/epjd/e2015-60644-y

Regular Article

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

¹ Department of Physics, St. Petersburg State University, Ulianovskaya 1, Petrodvorets, 198504 Saint Petersburg, Russia
² ITMO University, Kronverkskii ave 49, 197101 Saint Petersburg, Russia
³ Institut für Theoretische Physik, TU Dresden, 01062 Dresden, Germany

^a e-mail: aleliv12@mail.ru

Received: 13 November 2015
Received in final form: 5 December 2015
Published online: 21 January 2016

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 Z_cr ≈ 145. If the Hamiltonian contains both the recoil operator and the Uehling potential, the 1s level reaches the negative energy continuum at Z_cr ≈ 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.