TheZ-expansion of unrestricted Hartree-Fock atomic orbitals

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Abstract
It is shown, in agreement with Stewart, that in the open-shell (i.e. unrestricted) Hartree-Fock wave function for the ground state 1S of helium-like atoms, the two orbitals u, v have terms in Z-1/2, Z-3/2,... as well as Z-1, Z-2,..., when expanded in a perturbation series in powers of Z-1. But standard perturbation theory methods are not able to fix the orbitals uniquely. Consideration of the appropriate Hartree-Fock equations for u and v show that, in terms of Z, u(r, Z1/2) = v(r, - Z1/2). If u is expanded as u(r, Z) = u0(r) + Z-1/2u1/2(r) + Z-1u1(r) +... an approximate expression for u1/2 is {2Zr + 3)/4 [radical]2}u0.