Coulomb sum rule in the quasielastic region using various nuclear models

Abstract

We calculate the Coulomb sum rule of inclusive $(e,{e}^{\ensuremath{'}})$ reactions from $^{12}\mathrm{C}, ^{40}\mathrm{Ca}, ^{56}\mathrm{Fe}$, and $^{208}\mathrm{Pb}$ in the quasielastic region using various relativistic single-particle models, which include the relativistic Hartree, the nonlinear sigma, the quark-meson-coupling, and the chiral quark-meson-coupling models. We investigate the cross sections calculated in these nuclear models by comparing them with Bates, Saclay, and SLAC data for three-momentum transfer $q$ ranging from 300 to 500 $\mathrm{MeV}/c$. We find that the extracted longitudinal structure functions are not so sensitive to the nuclear model but the transverse structure functions strongly depend on the model. We report that, for three-momentum transfer $q>400 \mathrm{MeV}/c$, the values of the Coulomb sum rule from various nuclear models except the Hartree model are greater than 1.