Mean, median, and mode of R2.

The energy information of pulse signals is significantly important for applications such as computed tomography (CT), positron emission tomography (PET), and research on defects in condensed matter. Time-over-threshold (TOT) and multi-voltage threshold (MVT) are commonly used digitization methods in sampling pulse signal. However, both approaches rely on a mathematical model of the pulse signal to derive energy information. This study proposes a semi-empirical mathematical model for pulse signals formation process in scintillation crystal-coupled photomultiplier tube(PMT) probes, by utilizing the CR-RC shaping method. This mathematical model accurately describes output of the PMT pulse signals. This study analyzes a substantial dataset of pulse signals, comparing the performance of the newly designed mathematical model with that of the double exponential function in terms of their ability to fit pulse signals. The results indicate that the mathematical model developed herein achieves an average R2 of 0.9255, significantly surpassing the 0.9155 of the double exponential function, thereby demonstrating its superior fitting efficacy.