A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.