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 in R^3. Then, for any j in {1,…,M} and k in {1,…,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}{j,k}, phi^{(2)}{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}{j,k}(x) + |x - R_k| phi^{(2)}{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo–Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.