The longitudinal and transverse responses in the inclusive electron scattering: a functional approach

The splitting between the charge-longitudinal and spin-transverse responses is explained in a model whose inputs are the effective interactions in the particle-hole channels in the frame of the first order boson loop expansion. It is shown that the interplay between $\omega$-meson exchange and box diagrams (two-meson exchange with simultaneous excitation of one or two nucleons to $\Delta$'s) mainly rules the longitudinal response, while in the transverse one the direct $\Delta$ excitations almost cancel the one-loop correction and the response is mainly governed by the $\rho$-meson rescattering inside the nucleus. It is also shown that a small variation in the nuclear densities may explain the observed discrepancies between different nuclei.