The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

Abstract

We have performed a many-body calculation of the longitudinal nuclear (e, e ′ ) reaction employing a Second RPA (SRPA) formalism which contains the ∆(1232). More explicitly, our scheme contains RPA correlations as well as Hartree-Fock and second order self-energies, where an accurate evaluation of exchange terms is achieved. Using this formalism we have evaluated the longitudinal response function for 40 Ca. We give final results at momentum transfers ranging from 300 up to 500 MeV/c, obtaining a good agreement with data.PACS number: 21.65+f, 25.30.Fj, 21.60.Jz.

The longitudinal and transverse nuclear responses within the RPA framework

“…Even if there is a small tendency to overestimate data, these results certainly represent an improvement over the previous ones. In the recent work of [14] we report results for the 40 Ca longitudinal response, at momentum transfers ranging from 300 up to 500 MeV/c, in good agreement with data. In that work, a full antisymmetric second random phase approximation (SRPA) with the explicit inclusion of the (1232) was developed.…”

“…A large body of theoretical work has been done in order to solve this puzzle. Let us briefly mention that one point of view ascribes the problem to modifications of the nucleon properties within the nuclear medium (see [6]), while another perspective, followed in the present work, is based on the many-body theory performed in finite nuclei (see [7] and references therein) or in nuclear matter [8][9][10][11][12][13][14][15][16][17][18]. Fortunately, surface effects for heavy and medium nuclei in the energy-momentum region of interest are not very important and the nuclear matter formalism is a good approximation for the nuclear system, once an appropriate Fermi momentum or the local density approximation is used.…”