Heisenberg, who led the project, wrote in 1947 that the reactor lacked only a 'relatively small amount of uranium' to work. But research published in the journal PNAS Nexus argues he was off by a factor of about two.
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'My results argue that Heisenberg was off by roughly a factor of two,' said first author Patrick Park, a doctoral student at Princeton University who co-wrote the study while at Columbia University.
Park said Heisenberg's mistake was understandable: His calculations were only approximate, and the project was relocated to a rock cellar in the town of Haigerloch, Germany, after Berlin was bombed.
'People were dying or starving and so these reactor calculations were not his first priority,' while many details of neutron physics were unknown at that time, Park told Live Science in an email. 'Given these circumstances, I think he did the best he could.'
The B8 reactor consisted of five concentric circles of uranium cubes suspended on chains within a tank of heavy water. By combining archival records of the cubes, heavy water and graphite used by the German scientists with measurements of two surviving cubes, the researchers created a mathematical model of the reactor. It showed the reactor contained only about 370 gallons (1,400 litres) of heavy water, rather than more than 780 gallons (roughly 3,000 litres) needed, and about half the required uranium, 664 cubes totalling 3,390 pounds (1,540 kilograms), when at least 1,200 cubes would have been needed.
The study also examined whether the Germans could have built a graphite-moderated reactor instead, like the one developed in Chicago. The authors found that was impractical because German coal used to produce graphite contained high levels of neutron-absorbing boron.
'We conclude Germany could not have built heavy water nor graphite reactors during World War II,' the researchers wrote.
Mark Walker, a historian at Union College in New York and author of 'Hitler's Atomic Bomb,' who was not involved in the study, agreed that a graphite reactor was unfeasible but cautioned that the analysis is counterfactual. 'This paper argues that if the Germans had done something they did not do, then this would have failed,' he said. 'While this is counterfactual history, it is an interesting engineering analysis.'
