A unified quenching model in Geant 4 simulation for $\alpha$, proton and electron particles in liquid scintillator detectors
The liquid scintillator (LS) detectors are widely used in reactor neutrino experiments. To precisely measure the oscillated neutrino spectrum, it is crucial to understand the LS energy response, especially the quenching effect. Numerous bench-top measurements have been conducted on quenching effects for $\alpha$ particles, protons, and electrons. These results have typically been described by Birks' law, but with different Birks' coefficients required for different particle species. In this study, we find that if more secondary electrons are allowed to be generated in Geant4 simulations, the bench-top results for all particles can be well fitted using a single Birks' coefficient of about $0.013~{\rm g\,cm^{-2}\,MeV^{-1}}$. The underlying reason is that a large fraction of the primary energy is deposited through the generation of $\delta$-electrons with energies below 4~keV, which should be tracked separately due to their different quenching behavior compared to primary particles. This study provides a unified framework for comparing Birks' coefficients from different bench-top measurements and helps experiments like JUNO and SNO+ better tune their simulations for precision energy measurements.