Relativistic random-phase-approximation response function for quasielastic electron scattering in local density approximation

The longitudinal and transverse response functions for quasielastic electron scattering on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ are calculated in the relativistic σωρ model in random-phase approximation. We use space-dependent baryon densities and effective mass of the nucleons, as obtained from mean-field theory of closed-shell nuclei, in local-density approximation. The longitudinal response function agrees with experimental data quite well, while the transverse response function underestimates data. Our results are also compared with other calculations of the response functions in relativistic models.