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We prove that the Hartree--Fock orbitals of pseudorelativistic atoms, thatis, atoms where the kinetic energy of the electrons is given by thepseudorelativistic operator sqrt{-Delta+1}-1, are real analytic away from theorigin. As a consequence, the quantum mechanical ground state of such atoms isnever a Hartree-Fock state.  Our proof is inspired by the classical proof of analyticity by nested ballsof Morrey and Nirenberg. However, the technique has to be adapted to take careof the non-local pseudodifferential operator, the singularity of the potentialat the origin, and the non-linear terms in the equation.

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