Multiplicity Counting from Fission Detector Signals

A non-intrusive method of determining the properties of an unknown fissile item is to use the few lowest order factorial moments of the number of neutrons detected after one source event (a spontaneous fission, followed by internal multiplication inside the sample). These factorial moments are simply related to the counting rates of single, double and triple coincidences (“singles, doubles and triples count rates”), which are the measurable quantities. This method is based on counting statistics of discrete detector pulses, and is usually referred to as multiplicity counting. Because of inherent characteristics of the detection process, basically charge collection and signal pile-up, this method suffers from the so-called dead time effect, which is very difficult to account for in the case of doubles and triples.

An alternative method to multiplicity counting has been recently suggested by the present authors. The method uses the fission detector signals in the current mode to extract the same information about the fissile item as the traditional multiplicity counting methods from the singles, doubles and triples rates. Instead of the statistics of discrete pulses, the new method is based on the first three central moments of the time-resolved signals of one or more (up to three) fission chambers. The new method has certain advantages, primarily that it is free from the dead-time problem, hence it can be used at high count rates without dead-time corrections.

In this talk the theory of the method is described and it is shown how the same statistical information can be extracted from the continuous detector currents as from the discrete pulse counting method. First, a stochastic theory of the fission chamber signals is given. Then it is shown that with the use of the concept of “superfission” of Böhnel, and with the assumption of simultaneous detection of all neutrons originating in one source event, the same information can be extracted from the instantaneous detector signals, taken at the same time (“one-point distribution in time”) as from the multiplicity rates.

However, the assumption that all detections of neutrons from one source event are exactly simultaneous, represent a significant limitation, which is not fulfilled in reality. To eliminate this shortcoming, a random time distribution of the neutron arrival times to the detector is introduced. Exact analytical relationships are derived for the three auto- and cross-cumulants of the signals of up to three fission chambers, and it is shown that these are still uniquely and unambiguously related to the multiplicity rates. Hence the sample parameters still can be unfolded from these cumulants; the only difference is that in the unfolding formulas, the properties of the arrival time delay distribution also enter.

In the case of short time delays, which are comparable with the pulse width of the detector signal for a single detection, still all detector signals can be taken simultaneously. However, if the time delay of the detections is larger than the detector pulse width, two- and three-point (in time) distributions (temporal correlations) between the detector signals need to be considered in order that the various sample properties can be determined. Corresponding formulas, showing how the parameters of the sample can be determined from the signal statistics, are given and discussed.