Comment on 'predictions of critical radii for reactors and bombs 1939–45 including the Frisch–Peierls memorandum'

I showed in my recent EPJH paper that Peierls’ approximation for small fission reproduces neither the correct fission rate nor the correct diffusion coefficient. But Peierls’ result can be presented in a way that is superficially closer to Perrin’s correct result. Perrin’s paper motivated Peierls in the first place. Peierls did not reproduce Perrin’s reaction–diffusion equation to zeroth order, but rather only diffusion to lowest order. Perrin’s rate term allowing for non-fission neutron absorption appears to first order, but then only at the expense of an incorrect diffusion coefficient. As a byproduct of this analysis, we discover the reason for Peierls’ introduction of his strange second length scale, which otherwise would seem to have been obtained by a hat trick.