Multiplicity counting from fission detector signals with time delay effects

In recent work, we have developed the theory of using the first three auto- and joint central moments of the currents of up to three fission chambers to extract the singles, doubles and triples count rates of traditional multiplicity counting (Pazsit and Pal, 2016; Pazsit et al., 2016). The objective is to elaborate a method for determining the fissile mass, neutron multiplication, and ( α , n) neutron emission rate of an unknown assembly of fissile material from the statistics of the fission chamber signals, analogous to the traditional multiplicity counting methods with detectors in the pulse mode. Such a method would be an alternative to He-3 detector systems, which would be free from the dead time problems that would be encountered in high counting rate applications, for example the assay of spent nuclear fuel. A significant restriction of our previous work was that all neutrons born in a source event (spontaneous fission) were assumed to be detected simultaneously, which is not fulfilled in reality. In the present work, this restriction is eliminated, by assuming an independent, identically distributed random time delay for all neutrons arising from one source event. Expressions are derived for the same auto- and joint central moments of the detector current(s) as in the previous case, expressed with the singles, doubles, and triples ( S , D and T ) count rates. It is shown that if the time-dispersion of neutron detections is of the same order of magnitude as the detector pulse width, as they typically are in measurements of fast neutrons , the multiplicity rates can still be extracted from the moments of the detector current, although with more involved calibration factors. The presented formulae, and hence also the performance of the proposed method, are tested by both analytical models of the time delay as well as with numerical simulations. Methods are suggested also for the modification of the method for large time delay effects (for thermalised neutrons).