A general analytical solution for the variance-to-mean Feynman-alpha formulas for a two-group two-point, a two-group one-point and a one-group two-point cases

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