Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree-Fock) of Coulomb systems. We prove the following: let {phi(1),...,phi(M)} be any solution to the rank-M multiconfiguration equations for a molecule with L fixed nuclei at R-1,..., R-L is an element of R-3. Then, for any j is an element of {1,..., M}, k is an element of {1,..., L}, there exists a neighborhood U-j,U-k subset of R-3 of R-k, and functions phi((1))(j,k), phi((2))(j,k), real analytic in U-j,U-k, such that phi(j)(x) = phi((1))(j,k)(x) + vertical bar x - R-k vertical bar phi((2))(j,k)(x), x is an element of U-j,U-k. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo-Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schrodinger operator of atoms and molecules near two-particle coalescence points.