Hydrogen atom in a strong magnetic field. II. Relativistic corrections for low-lying excited states

Abstract

The highly accurate solution of the Schr\odinger equation in the form of common Landau exponential factor multiplied by a power series in two variables, the sine of the cone angle and radial variable is completed by the first-order relativistic correction calculated within the framework of the relativistic direct perturbation theory (DPT). It is found that in contrast to behavior of relativistic corrections for the ground state and ${2p}_{\ensuremath{-}1}{(m}_{s}=\ensuremath{-}1/2)$ excited state, which change sign from negative to positive near $B\ensuremath{\approx}{10}^{11}\mathrm{G}$ and $B\ensuremath{\approx}{10}^{10}\mathrm{G},$ respectively [Z. Chen and S. P. Goldman, Phys. Rev A $45,$ 1722 (1992)], the relativistic corrections for ${2s}_{0}{(m}_{s}=\ensuremath{-}1/2)$ and ${2p}_{0}{(m}_{s}=\ensuremath{-}1/2)$ excited states are negative for the magnetic field varying in range $0lBl{10}^{13}\mathrm{G}.$ If relativistic correction significantly mix nonrelativistic states the near-degenerate version of DPT is used. The avoided crossings of relativistic levels with $\ensuremath{\mu}=\ensuremath{-}1/2$ and $\ensuremath{\pi}=\ensuremath{-}1,$ evolving from field-free states with principal quantum numbers $n=2,3,4$ are presented.