A Simple Analytical Formulation of the Dancoff Correction

The Dancoff correction to the surface term of a resonance integral has hitherto required tedious numerical evaluation of a double integral in cylindrical geometry. A recognition of the functional dependence of the correction on moderator mean free path λ allows a great simplification. If 1 - C is the surface correction for two rods of radius, ρ, separated a distance d between centers, then where is a function monotonically increasing with d/ρ, for which a graph is given. A simple formula is also given for C of a hollow rod’s interior.