ИСТИНА

Relativistic atomic spectra are drastically modified by an external magnetic fields of the atomic order of magnitude 2.35x109 G which corresponds to the 106 up to 1015 G field range relevant to the thin atmospheres of the compact objects including white dwarfs, neutron stars, and magnitars. While the comprehensive data for a relativistic hydrogen have been available for some time, this is less the case for atoms and ions with more than one electron, which are of interest due to the features discovered in the thermal emission spectra of isolated neutron stars. Since the perturbative treatment of the magnetic effects fails miserably for such strength the precise ab initio description of many-electron atoms represents the challenge for the relativistic quantum theory. From this perspective, it turns out to be interesting to examine the same systems in the pure relativistic framework still bypassing the full quantum electrodynamical (QED) regime but addressing the retardation effects on the electron-electron interactions. In the present work we calculate the relativistic ground and several excited states for the H, Li, Be and B atoms in the magnetic field strengths up to 10 12G range using the Dirac-Coulomb-Gaunt Hamiltonian in the framework of purely relativistic FCI approach where the pair creation- annihilation problem was avoided grossly within the no-pair approximation. All computations were performed in the Slater type bispinoric basis set using the restricted kinetic balance approach. First of all, the construction of the one-electron basis was performed applying the solution of the hydrogen-like atom problem for the given field using for all considered cases. The computing of the no-pair FCI Hamiltonian on the positive energy states was invoked for the states with the select relativistic symmetries. In this case, the simplicity of the atomic problem allows to effectively evaluate all one- and two-electron integrals involved which are readily combined in the method's Hamiltonian matrix elements using the effective caching strategy. Moreover, we applied the Lanczos-inspired approach for the energy dispersion functional which have been already used for the relativistic hydrogen atom. As a result of the study, the relativistic dependencies for the ground and first excited states energies on the magnetic field strengths were obtained for all of the above-mentioned atoms. The calculations performed indicate the necessity to include relativistic corrections given the current numerical accuracy of the nonrelativistic results. Besides the lack of bounds on the energy, the basis set applied in this work was found to be not very efficient for very strong magnetic fields and small atomic numbers, although the basis set saturation is still available in the considered cases. The authors are grateful to the Russian Science Foundation for the financial support under Project 22-23-01180.