During World War II, the United States raced to build the atomic bomb partly because it feared Nazi Germany might get there first. A new scientific investigation now suggests Germany was nowhere near as close as its lead physicist liked to imply - a finding that will surprise absolutely no one who has read a history book, but which now comes with uranium cubes.

By examining surviving uranium cubes and previously documented historical evidence, researchers uncovered major limitations in Germany's final experimental nuclear reactor. The project wasn't merely missing a few odds and ends. According to the calculations, the reactor would have needed far more uranium and heavy water than Germany had available during the war.

The Manhattan Project, America's secret wartime atomic effort, was driven in part by the possibility that Nazi Germany might achieve a similar breakthrough first. Scientists understood that whoever got there first could gain an unprecedented military advantage - a reasonable concern at the time, though it turned out Germany was busy losing a different race entirely.

One possible route to an atomic bomb involved building a nuclear reactor capable of producing plutonium, a radioactive element usable in weapons. Inside a reactor, uranium atoms undergo nuclear fission - nuclei split apart, releasing energy and extra particles called neutrons. Under the right conditions, those neutrons trigger further fission, creating a sustained chain reaction. Getting that chain to sustain itself, it turns out, is the hard part.

Although Nazi Germany pursued nuclear research through a program known as the Uranprojekt, historians have long debated how close its scientists came to building a functioning reactor. The debate is now considerably less interesting.

Germany's final attempt was an experimental reactor called the B8 pile, built in 1945 under physicist Werner Heisenberg. The device used cubes of natural uranium suspended in heavy water - a specialized substance essential to controlling the nuclear reaction.

Heavy water looks much like ordinary water, except its hydrogen atoms contain an extra neutron. That subtle difference makes it useful in certain reactors, where it serves as a neutron moderator: it slows neutrons released during fission, and slower neutrons are more likely to trigger further fission in uranium, helping sustain the chain reaction.

For Germany, obtaining enough heavy water was a major obstacle. During the war, the only European facility capable of supplying what the German program needed was the Norsk Hydro plant in Vemork, Norway - which Germany controlled after occupying Norway in April 1940.

Recognizing the plant's importance to Germany's nuclear ambitions, Allied forces targeted it with sabotage and bombing. A major American bombing raid struck Vemork on November 16, 1943, contributing to the eventual end of heavy water production there. Nothing says "we take your reactor seriously" like repeatedly blowing up the one factory that keeps it running.

When American forces discovered and dismantled the B8 reactor in 1945, it had never achieved criticality - the point at which a chain reaction becomes self-sustaining, each generation of fission producing enough neutrons to maintain the next. Criticality is a basic requirement for operating a conventional reactor. Despite the ominous name, it doesn't mean the reactor is about to explode; it simply means the chain reaction can continue without an external neutron source.

Heisenberg, who led the German reactor effort, maintained that the B8 experiment had come close to that milestone. He argued the device needed only a relatively modest increase in uranium to become operational. A new study led by Timothy Koeth and colleagues challenges that assessment - which is a polite way of saying Heisenberg may have been rounding up.

The researchers examined two surviving cubes of natural uranium used in the German project. They also studied historical records, technical reports, correspondence, and other archival documents to reconstruct the reactor's capabilities and determine what it would have needed to work. Their findings paint a very different picture of Germany's nuclear progress.

According to their calculations, the B8 reactor would have required approximately twice as much uranium and more than twice as much heavy water as it actually contained to achieve a sustained nuclear chain reaction. Those quantities exceeded what Germany had available during the war. In particular, the heavy water needed was far beyond what the German program could obtain from its Norwegian supply.

The researchers also examined whether German scientists could have sidestepped the heavy water shortage by using graphite, a form of carbon that can also slow neutrons. That approach had worked for American scientists, who achieved the world's first controlled, sustained nuclear chain reaction using a graphite-moderated reactor in 1942.

But the graphite available in German-controlled territory contained impurities that made it unsuitable - notably traces of boron, which absorb neutrons that would otherwise help sustain the reaction, preventing criticality. So Germany couldn't simply swap graphite for heavy water and call it a day.

The findings suggest Heisenberg significantly underestimated how much additional material his reactor would have required. Rather than standing on the verge of a functioning reactor, German scientists faced shortages they could not overcome with the resources they had. The research also offers a clearer explanation for why Germany's nuclear program never made the transition from experimental designs to a working reactor capable of producing material for an atomic bomb.

Based on the designs and materials available during World War II, the researchers conclude that Nazi Germany lacked the resources to make either its heavy water reactor or a graphite-based alternative operational. More than eight decades later, the surviving uranium cubes have helped resolve a longstanding historical question - revealing just how far Nazi Germany remained from achieving a critical step toward an atomic bomb. Heisenberg's reputation, meanwhile, remains moderated.

Materials provided by PNAS Nexus. Note: Content may be edited for style and length.