http://arxiv.org/pdf/1304.7940.pdf
The dependence of the atomic energy levels on a superstrong magnetic field with account of a finite nucleus radius and mass At magnetic fields = 1016 Gauss the Coulomb potential of the nucleus becomes screened due to large irradiative corrections (B0 = 1013 G = 4:4_109 T). This leads in particular to the freezing of the ground state energy of the hydrogen atom at the value E0 = 1.7 keV [1, 2]. This statement is correct up to the values of the magnetic field at which the Landau radius becomes close to the radius of the nucleus. For hydrogen this happens at B = 1019 G, where the value of the proton charge radius R = 0:877 fm (see [3]) was used for numerical estimate. The approximation of a pointlike proton is not valid for B >1019 G, .
