Antisymmetrization of a mean-field theory of collisions

For a system of N-italic fermions with Hamiltonian s-italicc-italicr-italicH-italic we evaluate matrix elements of the T-italic matrix between arbitrary Slater determinants Vertical Barchi>,Vertical Barchi'>. The resulting variational equations are driven Hartree-Fock-like equations, with source terms as right-hand sides, due to the ''channels'' Vertical Barchi>,Vertical Barchi'>. The validity of this mean-field approximation is illustrated by a numerical example.