Extraction of the Coulomb Sum Rule, Transverse Enhancement, and Longitudinal Quenching from an Analysis of all Available e-${}^{12}$C and e-${}^{16}$O 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 photo-production 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 parameterizations 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 reasonable agreement with recent theoretical calculations.

Comments: 9 pages, 7 figures, revised version accepted for publication in Phys. Rev. D (letter)