Extraction of the Coulomb sum rule, transverse enhancement, and longitudinal quenching from an analysis of all available e−C12 and e−O16 cross section data

Abstract

We report on a phenomenological analysis of all available electron scattering data on $^{12}\mathrm{C}$ (about 6600 differential cross section measurements) and on $^{16}\mathrm{O}$ (about 250 measurements) within the framework of the quasielastic (QE) superscaling model (including Pauli blocking). All QE and inelastic cross section measurements are included down to the lowest momentum transfer $\mathbf{q}$ (including photoproduction data). We find that there is enhancement of the transverse QE response function (${R}_{T}^{QE}$) and quenching of the QE longitudinal response function (${R}_{L}^{QE}$) at low $\mathbf{q}$ (in addition to Pauli blocking). We extract parametrizations of a multiplicative low $\mathbf{q}$ ``longitudinal quenching factor'' and an additive ``transverse enhancement'' contribution. Additionally, we find that the excitation of nuclear states contribute significantly (up to 30%) to the Coulomb sum rule $SL(\mathbf{q})$. We extract the most accurate determination of $SL(\mathbf{q})$ to date and find it to be in disagreement with random phase approximation (RPA) based calculations but in reasonable agreement with recent theoretical calculations, such as ``first principle Green's function Monte Carlo.''