General formulae for the Feynman-α method with the bunching technique

Recently, the bunching technique has been widely utilized in the Feynman-α experiment using a multi-channel scaler (MCS) to measure the prompt neutron decay constant αp. Although the bunching technique enables us to perform efficient experiments, it was pointed out that an inherent count-loss process arises due to the channel advance time Δ between adjacent MCS channels. Through derivation of a Feynman-α variance-to-mean formula containing Δ by means of the multi-gate Pál-Bell equation, Yamane and Hayashi ([Yamane, Y. & Hayashi, Y. 1995]. Annals of Nuclear Energy, 22(8), 533) indicated that this count-loss process does not play any important roles when the channel advance time is much smaller than the dwell time T. However, the Δ/T ratio often becomes large in thermal systems at deep-subcritical states or fast ones, because the dwell time should be chosen to be much smaller than reciprocals of αp values for such systems. On the other hand, since the ratio of the dead time d of neutron detectors to the dwell time becomes also large when the Δ/T ratio is not small, the count-loss process due to the dead time cannot be neglected. Therefore, Feynman-α variance-to-mean and covariance-to-mean formulae containing both Δ and d were derived by means of the compound detection probabilities. Based on the covariance-to-mean formula, a new experimental technique was developed and examined at the Kyoto University Critical Assembly. The result of the examination indicated that one can measure exact αp values when Δ/T ratios are known, even though Δ/T and d/T ratios are not small.