  The Campbell theorem, relating the variance of the current of a fission
chamber (a "filtered Poisson process") to the intensity of the detection events
and to the detector pulse shape, becomes invalid when the neutrons generating
the fission chamber current are not independent. Recently a formalism was
developed by the present authors [1], by which the variance of the detector
current could be calculated for detecting neutrons in a subcritical multiplying
system, where the detection events are obviously not independent. In the
present paper, the previous formalism, which only accounted for prompt
neutrons, is generalised to account also for delayed neutrons. A rigorous
probabilistic analysis of the detector current was performed by using the same
simple, but realistic detector model as in the previous work. The results of
the present analysis made it possible to determine the bias of the traditional
Campbelling techniques both qualitatively and quantitatively. The results show
that the variance still remains proportional to the detection intensity, and is
thus suitable for the monitoring of the mean flux, but the calibration factor
between the variance and the detection intensity is an involved function of the
detector pulse shape and the subcritical reactivity of the system, which
diverges for critical systems.
