Hydrogen atom under a sequence of static multipole perturbations: Wave-function corrections

A closed-form expression is obtained for , where phi0 is the nonrelativistic hydrogenic ground state, V is a sum of static multipole perturbations of the form A/sub L/lr/sup L/P/sub l/, L> or =l, G = Q(E0-H0)-1Q is the projected static Green operator, and Q = 1-Vertical Barphi0>, where ]V/sub m/,V/sub m/-1,...,V1] is a set of static multipole perturbations. This quantity is of great interest in the computation of sum rules, high-order wave-function corrections due to multipole perturbations, and the adiabatic and nonadiabatic potentials in the scattering of a charged particle by a hydrogenic ion and in the interaction between a Rydberg electron and the core ion in high Rydberg states of heliumlike ions