Relativistic Strong Scott Conjecture: A Short Proof

Abstract

We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic energy $(c^2{p}^2+c^4{)}^{1/2}-c^2$ used already by Chandrasekhar. 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. We give a short proof of a recent result by the authors and Barry Simon showing the convergence of the density to the relativistic hydrogenic density on this scale.

References in corpus (1)

• The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction

Cited by in corpus (1)

• The Scott conjecture for large Coulomb systems: a review