Exact solutions to the Dirac equation in a strong electric field of point charge $Z|e|$ and an external Coulomb scalar field have been found. It is shown that, in the presence of a scalar field, the range of parameter values at which the corresponding Hamilton operator is Hermitian is substantially wider than in the absence of such a field. This makes it possible to correctly study the problem of the stability of quantum-electrodynamic vacuum with respect to the formation of electron—positron pairs in these fields.
Department of Theoretical Physics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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