One-Electron Energy Spectra of Heavy Highly Charged Quasimolecules: Finite-Basis-Set Approach

The generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous calculations. The analysis of the monopole approximation with two different choices of the origin is performed. Special attention is paid to the lead and xenon dimers, Pb82+–Pb82+–e− and Xe54+–Xe54+–e−, where the energies of the ground and several excited σ-states are presented in the wide range of internuclear distances. The developed method provides the quasicomplete finite basis set and allows for the construction of perturbation theory, including within the bound-state QED.

One-electron Energy Spectra of Heavy Highly Charged Quasimolecules

The generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous calculations. The analysis of the monopole approximation with two different choices of the origin is performed. Special attention is paid to the lead and xenon dimers, Pb82+–Pb82+–e− and Xe54+–Xe54+–e−, where the energies of the ground and several excited σ-states are presented in the wide range of internuclear distances. The developed method provides the quasicomplete finite basis set and allows for construction of the perturbation theory, including within the bound-state QED.

Расчет энергии и ширины сверхкритического резонанса в квазимолекуле урана

The energy and width of the supercritical resonance, which appears after the diving of the ground state of the uranium quasimolecule in the negative-energy Dirac continuum, are calculated. The calculations are performed taking into account the full two-center potential of the nuclei. The obtained results are compared with the corresponding values calculated in the monopole approximation and with taking into account the few lowest terms of the multipole expansion.

Vacuum fluctuation inside a star and their consequences for neutron stars, a simple model

Applying semi-classical quantum mechanics, the vacuum fluctuations within a star are determined, assuming a constant mass density and applying a monopole approximation. It is found that the density for the vacuum fluctuations does not only depend linearly on the mass density, as assumed in a former publication, where neutron stars up to 6 solar masses were obtained. This is used to propose a simple model on the dependence of the dark energy to the mass density, as a function of the radial distance [Formula: see text]. It is shown that stars with up to 200 solar masses can, in principle, be obtained. Though, we use a phenomenological model, it shows that in the presence of vacuum fluctuations stars with large masses can be stabilized and probably stars up to any mass can exist, which usually are identified as black holes.