The Transverse and Longitudinal Response Functions in ⁴He(e,e’) for the Range 0.55 GeV/c ≤ | q| ≤ 1.0 GeV/c

In electron scattering off a nuclear target, the Coulomb sum is defined as the integration of the longitudinal response function $R_L$ over the energy loss of the incident electron in the quasi-elastic nucleon knock-out process. The Coulomb Sum Rule states that at sufficient high three-momentum-transfer |\vec{q}|, the Coulomb sum should equal to the total number of protons in the nucleus: $S_L$ → 1. Previously, precision data existed only up to |$\vec{q}$| = 600 MeV/c due to the limited beam energy used, and one data point existed for |$\vec{q}$| = 1.14 GeV/c but with limited precision. During Jefferson Lab experiment E05-110, electron scattering cross sections were measured in the quasi-elastic region on $^4$He,$^{12}$C, $^{56}$Fe and $^{208}$Pb targets at four scattering angles (15, 60, 90, 120 degrees). The longitudinal and transverse response functions $R_L$ and $R_T$ were extracted in the momentum transfer range 0.55 GeV/c ≤ |$\vec{q}$| ≤ 1.0 GeV/c using the Rosenbluth separation method. The Coulomb sum was formed in the same |$\vec{q}$| range. The focus of this thesis is the extraction of $R _{L,T}$ from the $^4$He target data. Preliminary results on $R_{L,T}$ and the Coulomb sum $S_L$ for $^4$He will be presented. The Coulomb sum for $^4$He is found to be in good agreement with previous data, and still indicate quenching ($S_L$ < 1) for the |$\vec{q}$| region measured by this experiment.