  The electronic structure of an atom with Z <= 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 > 137 is inconsistent and physically meaningless
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 > 137 do not arise
if the Dirac Hamiltonian is correctly defined as a self-adjoint operator, see
[1]. In this article, we brie y 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.
  [1] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, Theor. Math. Phys. 150(1)
(2007) 34
