Equivalence of the Peierls and Serber Wartime Expressions for the Critical Radius of a Fissile Isotope

A 1939 integral equation analysis of criticality published by Rudolf Peierls is compared to Robert Serber’s differential equation approach as recorded in the Los Alamos Primer. Despite their very different appearances, the two formulations are shown to be identical in the limit where the neutron multiplicity is of order unity. An extra result of the analysis is an explicit series expansion expression for the critical radius derived from Serber’s approach.