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

We consider a large neutral atom of atomic number Z , modelled 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, we find that the density on this scale converges to the minimizer of the Thomas–Fermi functional of hydrogen as Z → ∞ when Z/c is fixed to a value not exceeding 2/π. This shows that the electron density on the Thomas–Fermi length scale does not exhibit any relativistic effects.