distinguished M.P. emphasized with a nod to Niels Bohr, held that “only a minor constituent of uranium is effective in these processes.” That constituent would need to be laboriously extracted for any large-scale effects. “The chain process can take place only if the uranium is concentrated in a large mass,” Churchill continued, slightly muddling the point. “As soon as the energy develops, it will explode with a mild detonation before any really violent effects can be produced. It might be as good as our present-day explosives, but it is unlikely to produce anything very much more dangerous.” He concluded optimistically: “Dark hints will be dropped and terrifying whispers will be assiduously circulated, but it is to be hoped that nobody will be taken in by them.”
Frisch found a friend that year in a fellow emigrd at Birmingham, the theoretician Rudolf Peierls. A well-off Berliner, a slender man with a boyish face, a notable overbite and a mind of mathematical austerity, Peierls was born in 1907 and had arrived in England in 1933 on a Rockefeller Fellowship to Cambridge. With the Nazi purge of the German universities he chose to remain in England. He would be naturalized as a British citizen in February 1940, but until then he was technically an enemy alien. When Oliphant consulted with him from time to time on the mathematics of resonant cavities — important for microwave radar — both men were careful to pretend that the question was purely academic.
Peierls had already contributed significantly to the debate on the possible explosive effects of fission. The previous May one of Frederic Joliot's associates in Paris, Francis Perrin, had published a first approximate formula for calculating the critical mass of uranium — the amount of uranium necessary to sustain a chain reaction. A lump smaller than a critical mass would be inert; a lump of critical size would explode spontaneously upon assembly.
The possibility of a critical mass is anchored in the fact that the surface area of a sphere increases more slowly with increasing radius than does the volume (as nearly
Peierls saw immediately that he could sharpen Perrin's formula. He did so in a theoretical paper he worked out in May and early June 1939 that the Cambridge Philosophical Society published in its
The USSR opportunistically invaded Finland at the end of November. In the rest of Europe the strange standoff prevailed that isolationist Idaho senator William Borah would label the “phony war.” The Peierlses moved to a larger house; early in the new year they generously invited Frisch to live with them. Genia Peierls, who was Russian, took the bachelor Austrian in hand. She “ran her house,” writes Frisch, “with cheerful intelligence, a ringing Manchester voice and a Russian's sovereign disregard of the definite article. She taught me to shave every day and to dry dishes as fast as she washed them, a skill that has come in useful many times since.” Life at the Peierlses was entertaining, but Frisch walked home through ominous blackouts so dark that he sometimes stumbled over roadside benches and could distinguish fellow pedestrians only by the glow of the luminous cards they had taken to wearing in their hatbands. Thus reminded of the continuing threat of German bombing, he found himself questioning his confident Chemical Society review: “Is that really true what I have written?”
Sometime in February 1940 he looked again. There had always been four possible mechanisms for an explosive chain reaction in uranium:
(1) slow-neutron fission of U238;
(2) fast-neutron fission of U238;
(3) slow-neutron fission of U235; and
(4) fast-neutron fission of U235.
Bohr's logical distinction between U238 and thorium on the one hand and U235 on the other ruled out (1): U238 was not fissioned by slow neutrons. (2) was inefficient because of scattering and the parasitic effects of the capture resonance of U238. (3) was possibly applicable to power production but too slow for a practical weapon. But what about (4)? Apparently no one in Britain, France or the United States had asked the question quite that way before.
If Frisch now glimpsed an opening into those depths he did so because he had looked carefully at isotope separation and had decided it could be accomplished even with so fugitive an isotope as U235. He was therefore prepared to consider the behavior of the pure substance unalloyed with U238, as Bohr, Fermi and even Szilard had not yet been. “I wondered — assuming that my Clusius separation tube worked well — if one could use a number of such tubes to produce enough uranium-235 to make a truly explosive chain reaction possible, not dependent on slow neutrons. How much of the isotope would be needed?”
He shared the problem with Peierls. Peierls had his critical-mass formula. In this case it required the cross section for fast-neutron fission of U235, a number no one knew because no one had yet separated a sufficient amount of the rare isotope to determine its cross section by experiment, the only way the number could be reliably known. Nevertheless, says Peierls, “we had read the paper of Bohr and Wheeler and had understood it, and it seemed to convince us that in those circumstances for neutrons in U235 the cross-section would be dominated by fission.” Peierls could state simply what followed: “If a neutron hit the [U235] nucleus something was bound to happen.”
What followed thus made the cross section intuitively obvious: it would be more or less the same as the familiar cross section that expressed the odds of hitting the uranium nucleus with a neutron at all — the geometric cross section, 10–23 square centimeters, an entire order of magnitude larger than the fission cross sections previously estimated for natural uranium that were small multiples of 10–24.
“Just sort of playfully,” Frisch writes, he plugged 10–23 cm2 into Peierls' formula. “To my amazement” the answer “was very much smaller than I had expected; it was not a matter of tons, but something like a pound or two.” A volume less than a golf ball for a substance so heavy as uranium.
But would that pound or two explode or fizzle? Peierls easily produced an estimate. The chain reaction would have to proceed faster than the vaporizing and swelling of the heating metal ball. Peierls calculated the time between neutron generations, between 1?2?4?8?l6?32?64…,to be about four millionths of a second, much faster than the several thousandths of a second Frisch had estimated for slow-neutron fission.
Then how destructive was the consequent explosion? Some eighty generations of neutrons — as many as could be expected to multiply before the swelling explosion separated the atoms of U235 enough to stop the chain reaction — still millionths of a second in total, gave temperatures as hot as the interior of the sun, pressures greater than the center of the earth where iron flows as a liquid. “I worked out the results of what such a nuclear explosion would be,” says Peierls. “Both Frisch and I were staggered by them.”
And finally, practically: could even a few pounds of U235 be separated from U238? Frisch writes:
I had worked out the possible efficiency of my separation system with the help of Clusius's formula, and we came to the conclusion that with something like a hundred thousand similar separation tubes one might produce a pound of reasonably pure uranium-235 in a modest time, measured in weeks. At that point we stared at each other and realized that an atomic bomb might after all be possible.
“The cost of such a plant,” Frisch adds for perspective, “would be insignificant compared with the cost of the war.”
“Look, shouldn't somebody know about that?” Frisch then asked Peierls. They hastened their calculations to Mark Oliphant. “They convinced me,” Oliphant testifies. He told them to write it all down.
They did, succinctly, in two parts, one part three typewritten pages, the other even briefer. Talking about it made them nervous, Peierls recalls (by then it was March and the exceptional cold had given way to warmer
