Stationary solutions of the second-order equation for fermions in the external Coulomb field

Self-conjugate second-order equations with spinor wave functions were examined for fermions moving in the external Coulomb field. For stationary states, the equations are characterized by separated states with positive and negative energies. This leads to the possibility of probability interpretation. For the Coulomb field of attraction, the energy spectrum of the second-order equation coincides with the spectrum of the Dirac equation while the probability densities being somewhat different. For the Coulomb field of repulsion, there exists an impenetrable potential barrier whose radius depends on the classical radius of an electron and on the electron energy. Existence of the impenetrable barrier is consistent with the experimental results on studying the internal electron structure and has no effect on the cross-section of the Coulomb electron scattering in the lower order of the perturbation theory. Availability of the impenetrable barrier can lead to confinement of positrons in supercritical nuclei with $Z \geqslant 170$ when spontaneous emission of vacuum electron-positron pairs occurs.