Exchange perturbation theory, III. Hirschfelder-Silbey type

An exchange perturbation theory is developed which yields in infinite order the same primitive function $F$ that is found in infinite order with the Hirschfelder-Silbey (HS) theory. The perturbation equations are identical to the HS equations only through first order. This is because the perturbing potential in our theory is not the bare interaction potential of the HS theory, but rather that potential screened by a nonlocal potential. The screening is the weakest that we have found in studying the equations satisfied by primitive functions, which are least distorted from products of the functions for the subsystems when the interactions have been turned off. We argue that this HS-type theory is best used when the interactions are weak.