The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian

Abstract

We consider a large neutral atom of atomic number $Z$, modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas--Fermi length scale $Z^{-1/3}$. Using an observation by Fefferman and Seco (1989), we find that the density on this scale converges to the minimizer of the Thomas--Fermi functional of hydrogen as $Z\to \infty$ when $Z/c$ is fixed to a value not exceeding $2/\pi$. This shows that the electron density on the Thomas--Fermi length scale does not exhibit any relativistic effects.

References in corpus (4)

• The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction
• The large-Z behaviour of pseudo-relativistic atoms
• The Ground State Energy of Heavy Atoms According to Brown and Ravenhall: Absence of Relativistic Effects in Leading Order
• The Ground State Energy of Heavy Atoms: the Leading Correction

Cited by in corpus (2)

• Seven Useful Questions in Density Functional Theory
• The Scott conjecture for large Coulomb systems: a review