The calculation of removal cross-sections between overlapping thermal groups

The use of two overlapping thermal groups has been recommended by a number of authors for the study of problems such as the variation of thermal spectra across lattice cells and flux peaking in water gaps. In this paper, the Kottwitz problem (two semi-infinite media at different temperatures, with neither sources nor absorption present) is used as an example, and three different methods for calculating the removal cross-sections between the groups are presented. Numerical values for the removal cross-sections are quoted using the free gas model of thermalisation.. If the diffusion coefficient of a medium is independent of energy, its removal cross-sections are found to be independent of temperature; even in H2O the temperature dependence of these cross-sections is (assuming the Radkowsky prescription) quite weak. The work requires extending to situations with finite absorption, and more sophisticated models of thermalisation should be used. (author)