The Intrinsic Energy Resolution of LaBr$_3$(Ce) Crystal for GECAM
This study aims to provide an accurate estimation of the intrinsic resolution of LaBr$_3$(Ce) crystal through a combination of experimental and simulation methods. We re-analyzed the data from previous Wide-Angle Compton Coincidence (WACC) and Hard X-ray Calibration Facility (HXCF) experiments, conducted PMT Single-Photoelectron Calibration (SPEC) and radial non-uniformity (also called Spot Scanning, SS) experiments to acquire new data, and combined these results with Geant4 simulations to isolate the contribution of each physical process to the total energy resolution, thereby allowing for a precise estimation of the scintillator's intrinsic resolution. For 100 keV X-rays, the total energy resolution of LaBr$_3$(Ce) crystal is 3.99% $\pm$ 0.04% (expressed as 1-$\sigma$), with statistical fluctuations and intrinsic resolution as the main components, contributing 2.47% $\pm$ 0.00% and 3.06% $\pm$ 0.06%, respectively. We identify two main sources of intrinsic resolution: one primarily due to non-proportional scintillation, contributing 2.28% $\pm$ 0.00%, and the other due to fluctuations in the energy transfer process, contributing 2.04% $\pm$ 0.08%. We quantified six components of the total energy resolution and reconstructed the photon response using Geant4. The consistency between the reconstructed relative light yield and the experimental measurements validated the mass model of the LaBr$_3$(Ce) detector used in the simulations.