An analytically soluble model for the mean field theory of collisions

A variational principle is used for the calculation of the matrix element of a resolvent operator (E-H)-1. Trial functions restricted to products of single particle orbitals generate driven, Hartree-Fock-like equations, with a right-hand side. We find a soluble model where these nonlinear equations reduce to the search for the roots of a 5th degree polynomial. One of the roots is always acceptable and generates an excellent numerical approximation. The theory has a regular on-shell limit. (orig.)