Asymptotics of the ground state energy in the relativistic settings

The paper is aimed at deriving sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, calculating the relativistic Scott correction term and also Dirac, Schwinger, and relativistic correction terms. Also it is proved that the Thomas–Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.