Related papers: Finite-Basis-Set Approach to the Two-Center Hetero…
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…
The electronic spectra of light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^2+$ and He$^+$-H$^+$ are analyzed. To this end, the two-center Dirac equation is solved by the dual-kinetically balanced finite-basis-set method for…
Ground-state energies of the one- and two-electron uranium dimers are calculated for internuclear distances in the range D=40--1000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for…
The problem of spontaneous vacuum decay in low-energy collisions of heavy nuclei is considered beyond the scope of the monopole approximation. The time-dependent Dirac equation is solved in a rotating coordinate system with $z$-axis…
The total energies of a large number of diatomic (or two-center) one-electron $A^{+} B^{+} e^{-}$ ions with unit electrical charges are determined numerically to high accuracy. Based on these results we derive some accurate…
A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion…
We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in Ref. [1]. For the calculations in Ref. [1], we constructed the basis…
We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case of unit nuclear charges is relevant for the accurate description of the ${\rm H}_2^+$ molecular ion and its isotopologues,…
We present a high-precision solution of Dirac equation by numerically solving the minmax two-center Dirac equation with the finite element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or…
A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…
A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated…
The Dirac equation for H$_2^+$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic…
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…
The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)] is extended to problems with a non-local spherically-symmetric…
A whole series of expressions for four species of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) is provided as a complete basis set to describe arbitrary single-centered spinful electron systems. A compact…
A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear…
Two approaches are developed for the study of the bound states of a one-dimensional Dirac equation with the potential consisting of $N$ $\delta$-function centers. One of these uses the Green's function method. This method is applicable to a…
A method, analogous to supersymmetry transformation in quantum mechanics, is developed for a particle in the lowest Landau level moving in an arbitrary potential. The method is applied to two-dimensional potentials formed by Dirac delta…
We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic…
In Coupled-Cluster (CC) theory, unphysical complex energies may arise in the presence of strong magnetic fields, near conical intersections, or in systems exhibiting complex Abelian point group symmetries. This issue originates from the…