Poisson's and Gaussian distribution of radioactive decay with Cobra4 (Influence of the dead time of the counter tube

1) The aim of this experiment is to show that the number of pulses counted during identical time intervals by a counter tube which bears a fixed distance to along-lived radiation emitter correspond to a Poisson´s distribution. A special characteristic of the Poisson´s distribution can be observed in the case of a small number of counts n 〈 20: The distribution is unsymmetrical, i. e. the maximum can be found among smaller numbers of pulses than the mean value. In order to show this unsymmetry the experiment is carried out with a short counting period and a sufficiently large gap between the emitter and the counter tube so that the average number of pulses counted becomes sufficiently small.

2) Not only the Poisson's distribution, but also the Guassian distribution which is always symmetrical is very suitable to approximate the pulse distribution measured by means of a long-lived radiation emitter and a counter tube arranged with a constant gap between each other.A premise for this is a sufficiently high number of pulses and a large sampling size. The purpose of the following experiment is to confirm these facts and to show that the statistical pulse distribution can even be approximated by a Guassian distribution, when (due to the dead time of the counter tube) counting errors occur leading to a distribution which deviates from the Poisson's distribution.

3) If the dead time of the counter tube is no longer small with regard to the average time interval between the counter tube pulses, the fluctuation of the pulses is smaller than in the case of a Poisson's distribution. In order to demonstrate these facts the limiting value of the mean value (expected value) is compared to the limiting value of the variance by means of a sufficiently large sampling size.