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

TL;DR

This paper analyzes extensive electron scattering data on carbon-12 and oxygen-16 using a quasielastic superscaling model, revealing transverse enhancement, longitudinal quenching, and contributions to the Coulomb Sum Rule, providing the most accurate measurements to date.

Contribution

It introduces phenomenological parameterizations for low-q longitudinal quenching and transverse enhancement, improving understanding of nuclear response functions in electron scattering.

Findings

Transverse QE response is enhanced at low q.

Longitudinal QE response is quenched at low q.

Nuclear state excitations contribute up to 30% to the Coulomb Sum Rule.

Abstract

We report on a phenomenological analysis of all available electron scattering data on ${\rm ^{12}C}$ (about 6600 differential cross section measurements) and on ${\rm ^{16}O}$ (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 $\bf q$ (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 $\bf q$ (in addition to Pauli blocking). We extract parameterizations of a $multiplicative$ low $\bf q$ "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 $SL({\bf q})$. We extract the most accurate determination of $SL({\bf q})$ to date and find it to be in reasonable agreement with recent theoretical calculations.