Nuclear matter Ward identity and the theory of final-state interactions in inclusive and exclusive reactions

We consider the response of a large nucleus, approximated by nuclear matter, to an electromagnetic probe at intermediate values of the momentum transfer, where nucleon knockout dominates the response. We discuss final-state interactions which may be included in the calculations of (e,e') inclusive reactions or (e,e'p) reactions, for example. We remark that the standard method for performing these calculations is inconsistent and address the question of the magnitude of the corrections required. We extend the discussion of Bentz, Arima, Hyuga, Shimizu, and Yazaki, who considered the role of the Ward-Takahashi identity in the calculation of the electromagnetic response in nuclear matter, to higher values of the momentum transfer. We suggest specific vertex corrections which should provide a more consistent formalism. We find that these corrections may be small in the vicinity of the quasielastic peak. However, definitive estimates of the corrections suggested here will require rather complex calculations. (It is of interest to note that the vertex correction is complex when the energetics are such that nucleon knockout is possible.)