A paper authored by Jeffrey E. Seifried and Ehud Greenspan, submitted to Nuclear Science and Engineering, published in September, 2015. LaTeX template was plucked from here.

An expression is derived for attributing the reactivity response due to perturbations to spectral, spatial, and isotopic effects. It is shown to be consistent at a global level with similar expressions derived in previous work, but can provide more detailed information on the physics phenomena contributing to the reactivity response of the perturbation. Using this expression, the reactivity effect of local coolant density perturbations -- local VCR -- are studied for two reduced-moderation BWR core designs: the RBWR-Th and RBWR-AC as well as for a standard ABWR. The RBWR core designs feature large axial variation in their neutron spectra.

The axial distribution of local VCR along the RBWR-Th seed and along the ABWR core were found to have the same general shape: negative throughout but most negative near the bottom and asymptotically approaching zero towards the top. However, the RBWR-Th VCR is roughly 4 times more negative. The RBWR-AC local VCR axial distribution varies greatly -- it is very close to zero in the seed regions and has a significant positive component in the central blanket.

Three effects were identified as contributing to the VCR due to a local water density change in the lower part of the RBWR-Th seed -- local spectrum hardening that tends to increase the local reproduction factor (eta-r) of each of the fuel isotopes; a redistribution of the local neutron absorption between the fuel isotopes resulting in a shift of absorptions from higher to lower isotopic reproduction factors and, hence, to a reactivity loss; and an axial flux tilt across the core from axial zones of higher eta-r to axial zones of lower eta-r which makes another negative contribution to the reactivity worth of the perturbation.