  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 non-local pseudodifferential operator, the singularity of the potential
at the origin, and the non-linear terms in the equation.
