Abstract
Derivation of an exact expression for calculating the first-flight collision probability in a regular lattice which consists of cylindrical fuel rods and moderator is presented. It is derived from extending the analysis of Dancoff and Ginsburg (1944) from a lattice of black absorbers to ones of finite cross section, this analysis being carried out without the simplifying approximation of the equivalent unit cell method of previous authors, by taking account of a closed trigonometrical formula for the optical neutron paths occurring in the lattice. The first-flight collision probability for a water-moderated rectangular lattice with a moderator to fuel volume ratio of 1:1 and a fuel rod diameter of 0366 in. is numerically calculated. The results are compared with those by the equivalent cylindrical unit cell method and various other approximations. It is concluded that the error introduced by cylindricalizing lattice cells in collision probability calculations for such a closely packed lattice is appreciable.
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