Influence of nucleonic motion in relativistic Fermi gas inclusive responses

Impulsive hadronic descriptions of electroweak processes in nuclei involve two distinctly different elements: one stems from the nuclear many-body physics — the medium — which is rather similar for the various inclusive response functions, and the other embodies the responses of the hadrons themselves to the electroweak probe and varies with the channel selected. In this Letter we investigate within the context of the relativistic Fermi gas in both the quasi-elastic and N→Δ regimes the interplay between these two elements. Specifically, we focus on expansions in the one small parameter in the problem, namely, the momentum of a nucleon in the initial wave function compared with the hadronic scale, the nucleon mass. Both parity-conserving and -violating inclusive responses are studied and the interplay between longitudinal (L) and transverse (T and T′) contributions is highlighted.