Relativistic calculations of the ground state energies and the critical distances for one-electron homonuclear quasi-molecules

TL;DR

This paper performs relativistic calculations of ground-state energies and critical distances for one-electron homonuclear quasi-molecules across a wide range of nuclear charges, using the Dirac-Fock-Sturm approach for both point and extended nuclei.

Contribution

It introduces a comprehensive relativistic computational method for calculating energies and critical distances in one-electron quasi-molecules with high nuclear charges.

Findings

Critical distances for Z=85-100 are determined.

Ground-state energies are calculated for Z=1-100.

Differences between point and extended nuclei cases are quantified.

Abstract

The ground-state energies of one-electron homonuclear quasi-molecules for the nuclear charge number in the range Z=1-100 at the "chemical" distances R= 2/Z (in a.u.) are calculated. The calculations are performed for both point- and extended-charge nucleus cases using the Dirac-Fock-Sturm approach with the basis functions constructed from the one-center Dirac-Sturm orbitals. The critical distances R_cr, at which the ground-state level reaches the edge of the negative-energy Dirac continuum, are calculated for homonuclear quasi-molecules in the range: Z=85-100. It is found that in case of U_2^{183+} the critical distance R_cr = 38.42 fm for the point-charge nuclei and R_cr = 34.72 fm for extended nuclei.