The Reaction Rate of Neutrons in a Maxwellian Medium

A general relation is derived for the reaction rate of neutrons of given speed with a Maxwellian distribution of nuclei. The expression is applicable to a cross section that varies with relative speed in an arbitrary manner and is shown to specialize to known results for 1/v absorption, a constant scattering cross section,  and resonance capture with Doppler broadening. Although the approach yields well-known results, it suggests the possibility of analytical unification of reactor theory for both research and pedagogical purposes.