Genius_ The Life and Science of Richard Feynman - James Gleick [101]
Bethe left the initial lectures trying to work out a way of calculating the efficiency of a nuclear explosion. Serber had presented a formula for the simplest case, when the mass of uranium or plutonium was just above critical. For bombs, which would require masses substantially over critical, the problem was far more difficult. He and Feynman developed a method of classic elegance that became known as the Bethe-Feynman formula. The dangerous practicalities of nuclear physics brought other questions. A lump of uranium or plutonium, even smaller than critical mass, raised the possibility of a runaway chain reaction—predetonation. Chemical explosives were far more stable. Bethe assigned this problem to Feynman in the project’s first months. Stray neutrons were always a presence, at some low level of probability—from cosmic rays, from spontaneous individual fissions, and from nuclear reactions caused by impurities. Cosmic rays alone sparked enough fission to make uranium 235 noticeably hotter in the high altitudes of Los Alamos than in sea-level laboratories. Without understanding predetonation, the scientists could not understand detonation itself, because they would not know how the bomb would behave during the split-second transition from subcritical to supercritical. Feynman spent a long time thinking about the properties of a chunk of matter in the peculiar condition of near-criticality, a form of matter that science had not had occasion to ponder before. He recognized that the essence of the problem was not its average behavior but its fluctuations: bursts of neutron activity here and there, spreading in chains before dying out.
Mathematics, in the form of probability theory, had barely begun to provide tools for handling such complex patterns; he discussed the problem with the Polish mathematician Stanislaw Ulam, and Ulam’s approach to it helped midwife a new field of probability called branching-processes theory. Feynman himself worked out a theory of fluctuations building upward from the easier-to-calculate probabilities of short chain reactions: a neutron splits one atom; a newly liberated neutron finds another target; but then the chain breaks. Some measurable fluctuations—audible bursts of noise on a Geiger counter—could be traced back to an origin in a single fission event. Others were combinations of chains. As with so many other problems, Feynman took a geometrical approach, considering the probability that a burst in a certain unit volume would lead to a burst in another unit volume at a given time later. He arrived at a practical method that reliably computed the chances of any premature reaction taking hold. It was suitable even for the odd-shaped segments of uranium that would be blasted into one another in the Hiroshima bomb.
Bethe found in Feynman the perfect foil and goad. This young man was quick, fearless, and ambitious. He was not satisfied to take away one problem and work on it; he wanted to work on everything at once. Bethe decided to make him a group leader, a position otherwise reserved for prominent physicists like Teller, Weisskopf, Serber, and the head of the British contingent at Los Alamos, Rudolf Peierls. For his part Feynman, who had lived through twenty-five years and a full formal education without ever falling under the spell of a mentor, began to love Hans Bethe.
Diffusion
Feynman did some recruiting for the project. He had invited one of his MIT fraternity friends to join the secret work. He even tried to recruit his father. Melville’s health had turned poor—his chronic high blood pressure affected him more and more—and Lucille wished he could afford to travel less. Richard wrote his mother that there might be a job available as a purchasing clerk. He wished, too, that Melville could