A Study on the Zero-Probability Method

Abstract

Let us consider the probabilities p (n, t) and p,,.(n, t). Here, p(n, t) is the probability that exactly n neutrons are found in the reactor at time t>O when a neutron had been injected at t=O, and p,.(n, t) the probability that a neutron detector placed in the reactor counts exactly m neutrons during a Lime interval (0, t) and exactly n neutrons are found at time t when a neutron had been injected at t=O. By formulating p(n, t) and p.,(n, t) in terms of last collision probabilities, linear partial differential equations for probability generating functions of p(n, t) and of Pm(n, t) have been derived. After solving these equations, the theory of zero-probability method is discussed. And it is shown that the probability P 0 (t) of recording no count during a time interval t is a function of a decay time constant a of prompt neutron chains and t. Moreover, an experiment has been carried out on an assembly containing slightly enriched uranium. Rossi-a measurements and pulsed neutron measurements have also been made for verification. The parameter a measured by the zero-probability method does not agree well with those by the other methods.

1/f Fluctuations on a Chain of Causal Relationships (Ⅰ); Formalization

“…In the model of this work, the statistics of particle number in a medium, in which a particle may branch into several particles, be captured or be observed by a detector in the presence of random particle immigration, are developed and the representations of time series are derived. A part of the present discussions is already developed in my previous works (3,4) .…”

“…(3)(4)(5)(6)(7)(8)(9) and the coefficient ( , , ) in Eq. (3-10) are easily obtained as( , , , ) = [(1 − − ) − ( − − )] × ( , , ) [(1 − ) − (1 − ) − ] − [ (1 − ) − (1 − ) − ]…”