Predictions of critical radii for reactors and bombs 1939–45 including the Frisch–Peierls memorandum

There were at least seven attempts to calculate critical radii for reactors or bombs 1939–1945. Those made by Flügge and Peierls in 1939 are compared with the calculations made by Perrin (1939), Heisenberg (1939 and 1945) and Serber (1943). Fermi’s 1942 reactor calculations are not covered here because that would call for a separate paper. Heisenberg calculated the critical radius formula and some critical radii in 1939 for a reactor. He focused on reactors 1939–45 and apparently did not make a bomb calculation before his August 1945 Farm Hall Lecture where he independently reproduced the 1943 Los Alamos Primer calculation for a bomb to within the limits that he knew the fast fission cross section. Flügge attempted a ponderous alternative to a critical radius calculation. Perrin’s calculation predates the Heisenberg and Serber calculations. His theoretical choice of tamper boundary condition was not optimal but his calculation method was correct. Peierls aimed to improve on Perrin's method but did worse. Finally, we calculate the 2.1 cm critical radius stated in the Frisch–Peierls Memorandum from Peierls’ model and graph, and we also show how Frisch and Peierls likely calculated it, including why Frisch assumed a fission cross section of 10 barn in his calculation.