Dead time corrections for inbeam γ-spectroscopy measurements

Relatively high counting rates were registered in a proton inelastic scattering experiment on 16O and 28Si using HPGe detectors which was performed at the Tandem facility of IFIN-HH, Bucharest. In consequence, dead time corrections were needed in order to determine the absolute γ-production cross sections. Considering that the real counting rate follows a Poisson distribution, the dead time correction procedure is reformulated in statistical terms. The arriving time interval between the incoming events (Δt) obeys an exponential distribution with a single parameter - the average of the associated Poisson distribution. We use this mathematical connection to calculate and implement the dead time corrections for the counting rates of the mentioned experiment. Also, exploiting an idea introduced by Pommé et al., we describe a consistent method for calculating the dead time correction which completely eludes the complicated problem of measuring the dead time of a given detection system. Several comparisons are made between the corrections implemented through this method and by using standard (phenomenological) dead time models and we show how these results were used for correcting our experimental cross sections.