francis perrin had defined a critical mass of uranium to be the smallest amount that could sustain a chain reaction, and had calculated the critical mass of uranium oxide (not metal) to be about . he reckoned that if a neutron reflector were placed around it of materials such as iron or lead which did not greatly impede fast neutrons, this might be reduced to . peierls also attempted to simplify the problem by using the fast neutrons produced by fission, thus omitting consideration of moderator. he then calculated the critical mass of a sphere of uranium metal in a theoretical paper written in 1939. he later recalled that the size of the critical mass "was of the order of tons. it therefore appeared to me that the paper had no relevance to a nuclear weapon."