Time-interval distributions in a digital gamma multi-channel analyzer at extreme input rates

This study explores the relationship between experimentally observed inter-event time-interval distributions (TIDs) and measured dead times for pulses generated by a HPGe gamma detector and processed by a digital spectrometer. The system utilizes a fast and slow channel, pileup rejector, trapezoid filtering, and flash analog-to-digital converter. The experimentally derived TIDs were compared with theory for validation. The results demonstrate that the theoretical model reliably describes measured TIDs up to 40% dead time. However, significant distortion effects become increasingly pronounced at higher input rates. It appears that the deviation between the measured and calculated TIDs take the shape of higher-order convolutions of the TID caused by an imperfection in the timing resolution in the pileup rejection circuit. In this work, theoretical functions for the TID are expanded to reproduce measurements up to 90% dead time. This refinement in the interpretation and treatment of the measured TIDs provides improved accuracy and precision in the prediction of the true event rate and measured dead time in the counter with results comparable to those from traditional methods. Although the new theoretical TIDs reflect processes that are specific to the experimental set-up, it is expected that similar adjustments are applicable to other gamma detection systems as well.