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We study the regularity at the positions of the (fixed) nuclei of solutionsto (non-relativistic) multiconfiguration equations (including Hartree--Fock) ofCoulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solutionto the rank--M multiconfiguration equations for a molecule with L fixed nucleiat R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, thereexists 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 similarresult holds for the corresponding electron density. The proof uses theKustaanheimo--Stiefel transformation, as applied earlier by the authors to thestudy of the eigenfunctions of the Schr"odinger operator of atoms and moleculesnear two-particle coalescence points.

Analytic structure of solutions to multiconfiguration equations