Distortion of neutron collision density due to resonance scattering and absorption

An analytical method for obtaining the collision density and the resonance integral in a homogeneous mixture of moderator and absorber is presented. The method incorporates ortho-normal expansion without any approximation such as narrow or wide resonance. A new ortho-normal set of functions of which the weight function is of shifted Breit-Wigner type is introduced for this purpose. Sample calculations are carried out for a mixture of ⁵⁹Co and heavy water, which is a typical case far removed from the two approximations mentioned. Comparison of the results with numerically obtained exact solutions shows that the first four terms of the expanded series are sufficient to express the collision densities in this case. (author)