Real analyticity away from the nucleus of pseudorelativistic Hartree–Fock orbitals

Abstract

We prove that the Hartree–Fock orbitals of pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator $\sqrt{-\Delta +1}-1$, are real analytic away from the origin. As a consequence, the quantum mechanical ground state of such atoms is never a Hartree–Fock state.

Our proof is inspired by the classical proof of analyticity by nested balls of Morrey and Nirenberg. However, the technique has to be adapted to take care of the nonlocal pseudodifferential operator, the singularity of the potential at the origin, and the nonlinear terms in the equation.