Time-interval distributions and counting statistics with a non-paralysable spectrometer

Time-interval density distributions of subsequently counted events with a non-paralysable spectrometer are scrutinised; a theoretical expression is presented and its results are compared with computer simulations of nuclear counting. The corresponding counting uncertainty formula is derived from the Laplace transform of the time-interval distribution formula. A clear difference is found in the counting statistics for the count integral of the full spectrum as compared to arbitrary fractions of the spectrum. New counting uncertainty formulas are presented for use in spectrometry. In addition, time-intervals and counting statistics are investigated theoretically for spectra taken with an ADC of the Wilkinson type, in which the characteristic non-extending deadtime varies linearly with the channel number.