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

We have performed a many-body calculation of the longitudinal nuclear $(e,e')$ reaction employing a Second RPA (SRPA) formalism which contains the $\Delta$(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.