Mass and Density, Criticality Relationships, Generalized

As it relates to neutron transport calculations, in an earlier report I defined scaling laws relating reactivity or criticality to the mass, density and dimensions of geometrically simple systems. Here I generalize these scaling laws to any geometry. These are well known relationships that allow the variation of critical mass versus density and/or dimensions to be written in a simple analytical form. With these relationships anyone can quickly estimate the critical mass corresponding to any given density, using nothing more complicated than a hand calculator. In addition I point out that these scaling laws can be used to easily predict the sensitivity of a system's K-eff to variations in density and/or dimensions. These relationships have appeared extensively in the literature for over 50 years, but seem to be periodically forgotten. As such, this report is not intended to present any new information, but rather it is intended merely to refresh our memories. The main idea is that you do not have to perform neutron transport calculations every time a parameter of a system is changed; instead you can use simple scaling laws to determine what will change. Here is a quick summary of results.