The stepwise time dependent backward Kolmogorov equation with delayed neutrons in counting statistics. Pt. 1

This paper is the first of two that deal with the moments up to the second order of the neutron counts taken in a time varying nuclear reactor. In the framework of the one-velocity point reactor model, explicitly taking into account the delayed neutrons, the backward Kolmogorov equation is used to study the branching process occurring in the system in which the kinetic parameters, the neutron detection efficiency and the source intensity may all be subject to arbitrary stepwise variations. Analytical rigorous expressions for the mean value and the variance of the counts measured in a time interval are obtained here, while the computation of the covariance between counts taken in two non-intersectiing intervals is deferred to the second paper. The variance-covariance matrix required to estimate parameters from experimental data will then be available. Numerical results concerning the mean value and the variance of the counts are reported and a FORTRAN IV program for computing the moments is available. (orig.)