Modification of Coulomb law and energy levels of the hydrogen atom in a superstrong magnetic field

We obtain the following analytical formula which describes the dependence of the electric potential of a pointlike charge on the distance away from it in the direction of an external magnetic field B: Φ(z)=e/|z|[1-exp(-√(6me2)|z|)+exp(-√((2/π)e3B+6me2)|z|)]. The deviation from Coulomb's law becomes essential for B>3πBcr/α=3πme2/e3≅6x1016 G. In such superstrong fields, electrons are ultrarelativistic except those which occupy the lowest Landau level (LLL) and which have the energy ε02=me2+pz2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B>3πBcr/α it differs substantially from the one obtained without accounting for the modification of the atomic potential.