  The intrinsic resolution is the primary limitation on the total energy
resolution of LaBr$_3$(Ce) crystal. This intrinsic resolution arises from two
effects: fluctuations occurring in the process of energy transfer to
luminescent centers within the LaBr$_3$(Ce) crystal and the LaBr$_3$(Ce)
crystal's non-proportional luminescence. Presently, experimental measurements
regarding the intrinsic resolution of LaBr$_3$(Ce) crystal are scarce, and the
underlying physical mechanisms remain incompletely understood. In this paper,
we aim to elucidate the concept of intrinsic resolution. We investigated the
entire physical process of luminescence following energy deposition in the
LaBr$_3$(Ce) crystal, quantifying the various components in the total energy
resolution. We conducted a series of experimental measurements and Geant4
simulations, determining the intrinsic resolution of LaBr$_3$(Ce) crystal to
100 keV electrons as 2.12%. The non-proportionality contributes significantly
at 1.43%, while fluctuations in the energy transfer process accounted for
0.27%. It is evident that non-proportionality in light output constitutes the
primary source of intrinsic resolution. Horizontal and vertical unevenness in
light collection contributed 0.25% and 0.07%, respectively. Statistical
fluctuations showed the largest impact on the total energy resolution, at
2.86%. The contribution from fluctuations in single-photoelectron events was
0.77%. Furthermore, we reconstructed the photon response using Geant4, and the
consistency between the simulated relative light yield and the experimentally
measured one confirmed the reliability of the LaBr$_3$(Ce) detector mass model
employed in the simulation.
