Ground‐state energy of uranium diatomic quasimolecules with one and two electrons

Abstract

Ground-state energies of the one-and two-electron uranium dimers are calculated for internuclear distances in the range = 40-1000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac equation without the partial-wave expansion for the potential of two nuclei. The one-electron one-loop QED contributions (self-energy and vacuum polarization) to the ground-state energy are evaluated using the monopole approximation for the two-center potential. Interelectronic interaction of the first and second order is taken into account for the two-electron quasimolecule. Within the QED approach one-photon-exchange contribution is calculated in the two-center potential, while the two-photon-exchange contribution is treated in the monopole approximation.

One-electron Energy Spectra of Heavy Highly Charged Quasimolecules

“…The results for the ground state of uranium dimers with one and two electrons were already presented in Ref. [40]. In this work, we extend the one-electron calculations to the lowest excited σ-states and present the results for the one-electron dimers, Pb 82+ -Pb 82+ -e − and Xe 54+ -Xe 54+ -e − .…”

“…As one can see from these data, except for the regions where MA(1) − MA(2) is anomaly small due to the sign change, it is comparable to TC(1) − MA(1). This observation can be used to quantify the inaccuracy of the MA for the contributions, which are not yet available for the TC calculations, e.g., the two-photon-exchange and QED corrections [40].…”

“…In Ref. [40] we have adapted the A-DKB method to diatomic systems, which also possess axial symmetry. Below we provide a brief description of the calculation scheme.…”

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

“…This case was also considered within this method in [46][47][48] to evaluate the higher-order contributions to the Zeeman splitting in highly charged ions. In [41], we adapted the A-DKB method to diatomic systems, which also possess axial symmetry. Below, we provide a brief description of the calculation scheme.…”

“…We consider the method based on the dual-kinetic-balanced finitebasis-set expansion [39] of the electron wave function for axially symmetric systems [40]. The results for the ground state of uranium dimers with one and two electrons were already presented in [41]. In the present work, we extend the one-electron calculations to the lowest excited σ-states and present the results for the one-electron dimers, Pb 82+ -Pb 82+ -e − and Xe 54+ -Xe 54+ -e − .…”