Neutron Counting Statistics in the Family-First-Pulse-Triggered Gate, (II)

Abstract

Statistic formulation of the neutron counts registered in a gate triggered by the family-first-pulse—which corresponds to the accumulated data in the usual Rossi-α experiment—is extended to the second moment. The second factorial moment <(c(c–1)> of neutron counts which are correlated with the trigger pulse is expressed as a function of the gate width and of the waiting time from the family-birth to the triggering; and it is shown that the function cannot be divided to contain the two variables separately. Neutron counts uncorrelated with the trigger pulse are analyzed into two components, and the second factorial cumulant <c(c–1)>–<c>2 of that originating from the families born before the trigger is shown to manifest the same dependence on gate width as that of correlated counts, with an amplitude ratio identical with the first moments. The uncorrelated counts of the second kind originating from the families newly born after the trigger present a somewhat different relation to the gate width, and hence constitute what are for practical purpose the only truly uncorrelated counts. The second factorial cumulant of the all-inclusive (correlated as well as the two kinds of uncorrelated) counts in stationary neutron field is formulated. Considerations are also presented on the effect of differences in the detector efficiency on the expected number of correlated count pairs in one gate.