Electronic structure of super heavy atoms revisited

The electronic structure of an atom with Z <= Z(c) = 137 can be described by the Dirac equation with the Coulomb field of a point charge Ze. It was believed that the Dirac equation with Z > Z(c) poses difficulties because the formula for the lower energy level of the Dirac Hamiltonian formally gives imaginary eigenvalues. But a strict mathematical consideration shows that difficulties with the electronic spectrum for Z > Z(c) do not arise if the Dirac Hamiltonian is correctly defined as a self-adjoint operator. In this paper, we briefly summarize the main physical results of that consideration in a form suitable for physicists with some additional new details and numerical calculations of the electronic spectra.