Superscaling analysis of the Coulomb Sum Rule in quasielastic electron-nucleus scattering

The Coulomb sum rule for inclusive quasielastic electron scattering in $^{12}$C, $^{40}$Ca and $^{56}$Fe is analyzed based on scaling and superscaling properties. Results obtained in the relativistic impulse approximation with various descriptions of the final state interactions are shown. A comparison with experimental data measured at Bates and Saclay is provided. The theoretical description based on strong scalar and vector terms present in the relativistic mean field, which has been shown to reproduce the experimental asymmetric superscaling function, leads to results that are in fair agreement with Bates data while it sizeably overestimates Saclay data. We find that the Coulomb sum rule for a momentum transfer $q\geq 500$ $MeV/c$ saturates to a value close to 0.9, being very similar for the three nuclear systems considered. This is in accordance with Bates data, which indicates that these show no significative quenching in the longitudinal response.