Two- and three-point (in time) statistics of fission chamber signals for multiplicity counting with thermal neutrons
Journal article, 2019
In two earlier papers Pazsit et al. (2016), Nagy et al. (2018) we investigated the possibility of extracting the traditional multiplicity count rates from the cumulants of fission chambers signals in the current mode. The first three cumulants for up to three fission chambers were derived in an extended stochastic model of the detector signals, introduced earlier for simpler problems Pal et al. (2014), Pal and Pazsit (2015). It was shown that if all neutrons emitted from the sample simultaneously are also detected simultaneously, the multiplicity rates can be retrieved from the cumulants of the detector current, but the method breaks down if the detections of neutrons of common origin take place with a time delay spread wider than the pulse shape. It was seen that even if the pulses overlap partially, the retrieval of the multiplicity rates depends on the time delay distribution, which is usually not known. To remedy these shortcomings, in this work we extended the theory from the previous one-point (in time) treatment, where all moments (cumulants) refer to the same time instant, to two- and three-point distributions (correlations). It was found that the integrals of suitably chosen two- and three-point moments with respect to the time differences become independent of the probability density of the time delays of detections. With this procedure, within practical limits, the multiplicity rates can be retrieved from the detector current(s) for arbitrary time delay distributions, and hence also with thermalised neutrons. The underlying theory, the outline of the derivations and the full results are given in the paper.