Vacuum polarization and the Coulomb sum rule

The longitudinal response function for quasielastic electron scattering from nuclear matter is calculated in a relativistic random phase approximation to the Walecka model including vacuum polarization effects. The Walecka model has nucleons interacting with isoscalar sigma and omega meson fields. The change in the vacuum polarization response of the Dirac sea because of the decrease in the relativistic effective mass of the nucleons leads to a thirty percent decrease in the energy integrated longitudinal response function (Coulomb sum rule). This change is isoscalar. Therefore, the transverse response, which is dominated by the isovector anomalous moment, is largely unchanged.