The Longitudinal and Transverse responses in inclusive electron scattering within the RPA framework

The longitudinal and transverse nuclear responses to inclusive electron scattering reactions are analyzed within the Random Phase Approximation (RPA) framework. Several residual interactions are considered and it is shown that the exchange terms in the RPA make very difficult to find an effective residual interaction capable of reproducing simultaneously the quasielastic peak of both the longitudinal and transverse responses. By means of a simplified model it is illustrated that the residual interaction used in a ring approximation must fulfill some restrictions in order to qualitatively reproduce the full RPA results