Heuristic derivation of Rossi-alpha formula with delayed neutrons and correlated source

Formulae of neutron correlation measurements, such as Feynmanand Rossi-alpha, have been derived in the past by the master equation method or the joint detection probability method. Generally speaking, the master equation method is rigorous in the sense. that all elementary processes can be taken into account, but its manipulations are complicated and elaborate. On the other hand, the method of joint detection probability is heuristic, but several kinds of formulae can be easily derived from it. It seems that these methods are complementary. Recently in order to develop a method for evaluating subcriticality in the accelerator driven subcritical reactors, we derived the Feynman-alpha formula with a correlated neutron source and delayed neutrons based on the master equation method. In this paper, based on a heuristic method, we have derived the joint detection probability including one group of delayed neutrons and a correlated neutron source, which is valid in deep subcritical systems. Then, as an application of this joint probability, the Rossi-alpha formula with delayed neutrons and a correlated neutron source has been derived.