On the role of the $Δ(1232)$ on the transverse nuclear response in the $(e,e')$ reaction

Abstract

The transverse nuclear response to an electromagnetic probe which is limited to create (or destroyed) a particle-hole ($ph$) or delta-hole ($Δh$) pair is analyzed. Correlations of the random phase approximation (RPA) type and self energy insertions are considered. For RPA correlations we have developed a scheme which includes explicitly the $Δ$ and the exchange terms. Self energy insertions over $ph$ and $Δh$ bubbles are studied. Several residual interactions based on a contact plus a ($π+ ρ$)-meson exchange potential are used. All calculations are performed in non-relativistic nuclear matter. The main effect of the $Δ$ is to reduce the intensity over the nuclear quasi-elastic peak. Exchange RPA terms are very important, while the self energy depends strongly on the residual interaction employed. We compare our final result with data for $^{40}Ca$ at momentum transfer $q=410$ and $q=550$ MeV/c.

42 pages, 18 Postscript figures