Proof of the Strong Scott Conjecture for Chandrasekhar Atoms

Abstract

We consider a large neutral atom of atomic number $Z$, taking relativistic effects into account by assuming the dispersion relation $\sqrt{c^2{p}^2+c^4}$. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the limit $Z,c\to \infty$ keeping $Z/c$ fixed and find that the spherically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the generalization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density.

35 pages; minor corrections in v.2; accepted for publication in Pure and Functional Analysis for the issue dedicated to the 85th birthday of Yasha Sinai