On the spectrum of the hydrogen atom in an ultrastrong magnetic field

Various approaches to computing the energies of the ground state and excited levels of the hydrogen atom in an ultrastrong magnetic field B that considerably exceeds the field B _a = m _e ² e ³ c/ħ ³ ∼ 10⁹ G are considered. The effects of polarization of vacuum and anomalous magnetic moment of the electron on the position of the atomic levels are discussed. The vacuum polarization effects are negligibly weak for B < 10¹⁵ G but become significant in fields B ≫ 10¹⁶ G, in which these effects qualitatively modify the atomic spectrum in this range. The difference in the behaviors of the even and odd energy levels for B ≫ B _a is analyzed and the formulas for the energies of odd levels as a function of field B are refined.