Influence of a superstrong external magnetic field on the electron energy spectrum in a strong Coulomb field and on the value of nucleus critical charge has been studied. Investigation has been reduced to solving the problem in a cut-off Coulomb field in $1+1$ dimensions. The Dirac equation in $1+1$ dimensions in an external scalar Coulomb field is shown to have a zero-energy nondegenerate charge-self-conjugate solution, and hence, the vacuum of the model should acquire a fermion charge ${\pm 1/2}$.
Department of General Physics and Molecular Electronics, Department of Theoretical Physics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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