Coulomb sum rules in the relativistic Fermi gas model

Coulomb sum rules are studied in the framework of the Fermi gas model. A distinction is made between mathematical and observable sum rules. Differences between nonrelativistic and relativistic Fermi gas predictions are stressed. A method to deduce a Coulomb response function from the longitudinal response is proposed and tested numerically. This method is applied to the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ data to obtain the experimental Coulomb sum rule as a function of momentum transfer.