  This paper presents a full derivation of the variance-to-mean or
Feynman-alpha formula in a two energy group and two spatial region-treatment.
The derivation is based on the Chapman - Kolmogorov equation with the inclusion
of all possible neutron reactions and passage intensities between the two
regions. In addition, the two-group one-region and the two-region one-group
Feynman-alpha formulas, treated earlier in the literature for special cases,
are extended for further types and positions of detectors.We focus on the
possibility of using these theories for accelerator-driven systems and
applications in the safeguards domain, such as the differential
self-interrogation method and the differential die-away method. This is due to
the fact that the predictions from the models which are currently used do not
fully describe all the effects in the heavily reflected fast or thermal
systems. Therefore, in conclusion a comparative study of the two-group
two-region, the two-group one-region, the one-group two-region and the
one-group one-region Feynman-alpha models is discussed.
