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We obtain the following analytical formula which describes the dependence ofthe electric potential of a point-like charge on the distance away from it inthe direction of an external magnetic field B: \Phi(z) = e/|z| [ 1-exp(-\sqrt{6m_e^2}|z|) + exp(-\sqrt{(2/\pi) e^3 B + 6m_e^2} |z|) ]. Thedeviation from Coulomb's law becomes essential for B > 3\pi B_{cr}/\alpha = 3\pi m_e^2/e^3 \approx 6 10^{16} G. In such superstrong fields, electrons areultra-relativistic except those which occupy the lowest Landau level (LLL) andwhich have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on whichLLL splits in the presence of the atomic nucleus is found analytically. For B >3 \pi B_{cr}/\alpha, it substantially differs from the one obtained withoutaccounting for the modification of the atomic potential.

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