On some problems in the counting statistics of nuclear particles: Investigation of the dead time problems

The probabilistic aspects of the detection of nuclear particles are discussed with the application of the methods of renewal theory. It is assumed that the inter-event times in the investigated event series are independent, identically distributed random variables. The detector efficiency and various types of the dead time are accounted for. Exact analytical results are derived for the probability distribution functions, the expectations and the variances of the number of detected particles. Also, a precise analysis of the coincidence problem is given. The results should serve for the evaluation of the measurements in view of the dead time correction effects for the higher moments of the detector counts.