A relationship between the many - body theory of inelastic scattering and the distorted wave approximation ?

In this paper we show that the first-order results of the recent many-body theory of inelastic electron scattering (Csanak, Taylor and Yaris) can be derived quite simply by a direct application of the distorted-wave and random phase approximations to the usual expression for the inelastic scattering amplitude. The result is derived both in the second quantized formalism and by the standard application of the distorted-wave approximation coupled with the random phase approximation (RPA). The RPA (or time-dependent HartreeFock theory) just provides the transition density between the initial and inelastically excited states. Possible generalizations of the procedures are discussed.