On the transients of elastic moderation theory

A complete solution of the neutron slowing-down problem is developed for isotropic elastic scattering in an infinite homogeneous medium. An exact formula for obtaining all the complex roots of the transcendental equation is given. This, together with the exact nontrivial real root determined elsewhere, constitutes the exact solution of the problem. A general misconception about the application of these roots in the first collision interval is pointed out. Numerical results obtained for different magnitudes of absorption rates show agreement with more conventional solutions, like that of Teichmann. The number of terms in the infinite sum necessary for convergence depends on the relative magnitude of lethargy and the pre-assigned permissible error. Good results are obtained with a modest number of terms for small values of relative lethargy, but only with a few for larger values of u/.