Thomas {\O}stergaard S{\o}rensen
The large - $Z$ behaviour of pseudo-relativistic atoms
(165K, LaTeX with 1 PS figure)
ABSTRACT. In this paper we study the large - $Z$ behaviour of the ground
state energy of atoms with electrons having relativistic kinetic energy
$\sqrt{p^{2}c^{2}+m^{2}c^{4}}-mc^{2}$. We prove that to leading order
in $Z$ the energy is the same as in the non-relativistic case, given
by (non-relativistic) Thomas-Fermi theory. For the problem to make
sense, we keep the product $Z\alpha$ fixed (here $\alpha$ is Sommerfeld's fine structure constant), and smaller than, or equal to, $2/\pi$, which means that as $Z$ tends to infinity, $\alpha$ tends to zero.