  We prove analytic-type estimates in weighted Sobolev spaces on the
eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with
singular potentials, which includes the Hartree-Fock equations. Going beyond
classical results on the analyticity of the wavefunctions away from the nuclei,
we prove weighted estimates locally at each singular point, with precise
control of the derivatives of all orders.
  Our estimates have far-reaching consequences for the approximation of the
eigenfunctions of the problems considered, and they can be used to prove a
priori estimates on the numerical solution of such eigenvalue problems.
