Final State Interactions and Target Correlations in Inclusive (e, e′) Reactions

Abstract

The inclusive (e, e′) cross section is approximated in terms of one-body operators within a theoretical framework that combines Feshbach's projection operator and Green's function formalisms. Particular attention is paid to the electromagnetic sum rules and to the effects of antisymmetrization, final state interactions, and target correlations. In a first step, only bound residual states are included and the coherent part of the hadronic tensor is neglected; the final state interactions are taken into account by means of optical-model potentials, one for each level of the residual nucleus. In a second step, “total energy” and “kinetic energy” prescriptions are introduced to relate these optical-model potentials to that associated with the ground state of the residual nucleus. This allows one, in a third step, to extend the theory to include unbound residual states. The resulting expressions of the hadronic tensor are traces of a product of two factors. One factor takes into account the final state interactions by means of spectral functions related to the optical-model potential of the residual nucleus in its ground state. The other factor takes into account the target correlations through the one-body density matrix in the case of the total energy prescription, and through the target spectral function in the case of the kinetic energy prescription. These expressions fulfill the non-energy-weighted sum rule at high but not at low or medium momentum transfer. In a fourth step, the latter drawback is cured by including the coherent part of the hadronic tensor. The resulting approximations fulfill the non-energy-weighted sum rule for all values of the momentum transfer. They only involve one-body operators, but are nevertheless rather complicated. In a fifth step, it is argued that these expressions can be approximated by simpler and practical ones for momentum transfers larger than the Fermi momentum. It is emphasized that the final state interactions should be evaluated from a realistic approximation to the self-energy.