NaI (Tl) Calorimeter Calibration and Simulation for Coulomb Sum Rule Experiment in Hall-A at Jefferson Lab

A precision measurment of inclusive electron scattering cross sections was carried out at Jefferson Lab in the quasi-elastic region for ${}^4$He, ${}^{12}$C, ${}^{56}$Fe and ${}^{208}$Pb targets. Longitudinal ($R_L$) and transverse ($R_T$) response functions of nucleon were extracted in the momentum transfer range 0.55 GeV/c$\le$$\mathrm{\mid }q\mathrm{\mid }$$\le$1.0 GeV/c. To achieve the above goal, a NaI (Tl) calorimeter was used to distinguish good electrons from background including pions and low energy electrons rescattered from walls of the spectrometer magnets. Due to a large set of kinematics and changes in HV settings, a number of calibrations were performed for the NaI (Tl) detector. Corrections for a few blocks of NaI (Tl) with bad or no signal were applied. The resolution of NaI (Tl) detector after calibration reached $\frac{\delta E}{\sqrt{E}} \approx 3%$ at E=1 GeV. The performance of NaI (Tl) detector was compared with a simulation.