The interaction effect between two neutron absorbers using Wallaces method

The dependence of Galaninʹs constant on fuel-plate separation is studied. Galaninʹs constant aries in the source-sink method of lattice calculations and normally its value for an isolated fuel plate is used. Our calculations therefore enable the accuracy of that assumption to be assessed, to illustrate the problem, two absorbing and scattering plates, embedded in an infinite moderator and separated by a distance b are considered, with a source in the moderator region. The calculations are carried out via the integral form of the transport equation using the little-known method of Wallace. This approach enables the integral equation lo be cast into a particularly useful form for evaluation of the flux and absorption rate in the plates. A variational method and a numerical solution provide results that show that there are significanl deviations from the isolated plate approximation. Tables and figures are provided to illustrate these conclusions. In addition to the main result, we take the opportunity to show how Wallaceʹs method can be used to simplify the transport equation for an infinitely reflected slab reactor. We also obtain results for the flux in a halt-space in which there is a constant source, using a novel approximation procedure. Comparison with the exact result shows high aLciirncy.