Genius_ The Life and Science of Richard Feynman - James Gleick [104]
If the sun were a coolly radioactive metal ball a few inches across, with neutrons rattling about inside, it would start to look like a miniaturized version of the same problem. For a while this approach proved useful. Past a certain point, however, it broke down. Too many idealizing assumptions had to be made. In a real bomb, cobbled together from mostly purified uranium, surrounded by a shell of neutron-reflecting metal, the messy realities would defy the most advanced mathematics available. Neutrons would strike other neutrons with a wide range of possible energies. They might not scatter in every direction with equal probability. The bomb might not be a perfect sphere. The difference between these realities and the traditional oversimplifications arose in the first major problem assigned to Feynman’s group. Bethe had told them to evaluate an idea of Teller’s, the possibility of replacing pure uranium metal with uranium hydride, a compound of uranium and hydrogen. The hydride seemed to have advantages. For one, the neutron-slowing hydrogen would be built into the bomb material; less uranium would be needed. On the other hand, the substance was pyrophoric—it tended to burst spontaneously into flame. When the Los Alamos metallurgists got down to the work of making hydride chunks for testing, they set off as many as half a dozen small uranium fires a week. The hydride problem had one virtue. It pushed the theorists past the limits of their methods of calculating critical masses. To make a sound judgment of Teller’s idea they would have to invent new techniques. Before they considered the hydride, they had got by with methods based on an approximation of Fermi’s. They been able to assume, among other things, that neutrons would travel at a single characteristic velocity. In pure metal, or in the slow reaction of the water boiler, that assumption seemed to work out well enough. But in the odd atomic landscape of the hydride, with its molecules of giant uranium atoms bonded to two or three tiny hydrogen atoms, neutrons would fly about at every conceivable velocity, from very fast to very slow. No one had yet invented a way of computing critical mass when the velocities spread over such a wide range. Feynman solved that problem with a pair of approximations that worked like pincers. The method produced outer bounds for the answer: one estimate known to be too large and another known to be too small. The experience of actual computation showed that this would suffice: the pair of approximations were so close together that they gave an answer as accurate as was needed. As he drove the men in his group toward a new understanding of criticality (poaching sneakily, it seemed to them, on the territory of Serber’s group, T-2), he delivered up a series of insights that struck even Welton, who understood him best, as mystical. One day he declared that the whole problem would be solved if they could produce a table of so-called eigenvalues, characteristic values of energies, for the simplified model that T-2 had been using. That seemed an impossible leap, and the group said so, but they soon found that he was right again. For Teller’s scheme, the new model was fatal. The hydride was a dead end. Pure uranium and plutonium proved far more efficient in propagating a chain reaction.
In this way, amid these clusters of scientists, the theory of diffusion underwent a kind of scrutiny with few precedents in the annals of science. Elegant textbook formulations were examined, improved, and then discarded altogether. In their place came pragmatic