Joint Probability Distribution of Neutron Counts in Reactor Noise Analysis

The probability generating function of the counts obtained in an arbitrary sequence of time intervals and counters is derived in the framework of the one-velocity point-reactor model without delayed neutrons. The main feature of the method is that the multiple derivatives of the probability generating function, which provide the joint probabilities and the joint moments, can be easily calculated from recurrence relations. The procedure is well suited to computer programming, and, indeed, a Fortran IV program has been written. Some conditioned probability profiles and moments thereby obtained are reported.