Contribution of Nuclear Excitation Electromagnetic Form Factors in ${\rm ^{12}C}$ and ${\rm ^{16}O}$ to the Coulomb Sum Rule

TL;DR

This paper provides empirical parameterizations of nuclear excitation electromagnetic form factors for ${}^{12}C$ and ${}^{16}O$, quantifies their contribution to the Coulomb Sum Rule, and emphasizes their importance in precise electron scattering calculations.

Contribution

It introduces new empirical parameterizations of nuclear excitation form factors and assesses their impact on the Coulomb Sum Rule in ${}^{12}C$ and ${}^{16}O$, aiding theoretical modeling.

Findings

Nuclear excitations contribute significantly to the Coulomb Sum Rule at low momentum transfer.

Total excitation contributions in ${}^{12}C$ and ${}^{16}O$ are consistent within uncertainties.

Nuclear excitation effects should be included in radiative correction calculations for electron scattering.

Abstract

We report on empirical parameterizations of longitudinal and transverse nuclear excitation electromagnetic form factors in ${\rm ^{12}C}$ and ${\rm ^{16}O}$. We extract the contribution of nuclear excitations to the Normalized Inelastic Coulomb Sum Rule (\csr) as a function of momentum transfer $\bf q$ and find that it is significant (0.29$\pm$0.030 at $\bf q$= 0.22 GeV). The total contributions of nuclear excitations to $S_L({\bf q})$ in ${\rm ^{12}C}$ and ${\rm ^{16}O}$ are found to be equal within the uncertainties. Since the cross sections for nuclear excitations are significant, the radiative tails from nuclear excitations should be included in precise calculations of radiative corrections to quasielastic electron scattering at low $\bf q$ and deep-inelastic electron scattering at large energy transfers $\nu$. The parameterizations also serve as a benchmark in testing theoretical modeling of cross sections for excitation of nuclear states in electron and neutrino interactions on nuclear targets at low energies.