So, perhaps surprisingly, the US did try to literally patent the atomic bomb. Not only did it file patent applications covering the exact mechanisms detonated during World War II, it filed hundreds of patent application covering every aspect of their production and operation, covering work from the mining of uranium ore all the way to the specific do-dads on the bomb that allowed it to detonate successfully.

But here's the thing. Patents aren't secret. They are very public: the entire point of a patent is that in exchange for disclosure of the idea, the person or company to whom the patent is granted is given a temporary monopoly on its manufacture. So it's sort of the opposite of secrecy. And, of course, if the USSR or some other nature build their own bombs, it's not like the US would sue them for royalties, or that this would be some kind of serious deterrent to nuclear proliferation.

Which leads to the question: how and why did they patent the atomic bomb? And the answer to "how" is: they used secret patent applications (kept secret under a WWI-era law). And the answer to "why" is: these patents were all assigned to the US government, which meant that the individual inventors (the scientists, engineers, etc.) involved were essentially relinquishing any legal rights to their inventions to the government, and it would help insulate the US government from anybody suing them for using any of these technologies (e.g., there were competing claims for a patent on nuclear reactors by French scientists, and the US didn't want to let the French tell them what they could or couldn't do with reactors). Anyway, it's an interesting story about the legal means to controlling technology and how during World War II, the people involved in the Manhattan Project had really no clue what the postwar situation would look like, so they sought to protect the government's legal position in any way possible, including this unusual and ambitious secret patenting program, one that was responsible for about 1% of all patent applications received by the US Patent Office during World War II (because that's how big the Manhattan Project was). In the postwar, Congress got so spooked and weirded-out by the whole program that they passed a law which said, among other things, that nuclear weapons are fundamentally un-patentable in the United States — they are the only category of real technology that is excluded from patentability by law. Anyway, there's so much more that can be said on all of this. If you are interested, I am probably one of the only people in the world who can answer deep follow-ups on this, because I literally wrote the paper on it: ["Patenting the Bomb: Nuclear Weapons, Intellectual Property, and Technological Control"](https://alexwellerstein.com/publications/wellerstein_patentingthebomb(isis).pdf).

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OK, that isn't really your question though, because I took the word patent as literal in an excuse to write about all of the above because I find it fascinating and it is still pretty obscure and I wrote a literal academic article on it. :-)

I would reframe your actual question as: why didn't the US find a way to prevent the spread of nuclear technology? And the answer is: they tried, in several ways! One way was to try and keep it quite secret. But there is "formula" of nuclear bombs. It is not that kind of bomb. The science that is the basis of an atomic bomb was public knowledge before the bombs were created, and the very existence of said bombs — made clear by their use above two Japanese cities — would have revealed quite a lot to other scientists and government about how one would go about making them. The US opted to release quite a bit of "sanitized" information about what it had done, both because it figured this was stuff that would come out anyway (if it wasn't already out there), but also because they both wanted there to be an informed discussion domestically and globally about "what to do next" and because they calculated that trying to keep the whole thing secret would probably release in people leaking the information (so it was better to make clear what information was "safe").

From the beginning, the scientists and statesmen involved in making the bomb more or less agreed that secrecy wasn't going to be all that likely to be successful, because, again, atomic bombs are essentially based on scientific facts, and any well-funded group of scientists can figure out those facts. Secrecy would, at best, just slow things down and increase the costs, but if the stakes of national survival were involved, then you'd expect all of that to not be a big hurdle, as it wasn't that big of a hurdle for the US itself (which built its bombs in only about 2.5 years of serious effort).

There were two main approaches taken to try and stop other states from getting atomic bombs. The first was a secret one: the US (and UK) tried to buy up all known uranium and thorium stockpiles in the world, under the hope that these key resources were relatively rare, and as a result, "starve" any other nuclear programs of these necessary products. Without large amounts of uranium (or, to a lesser degree, thorium) you can't have a nuclear program — it is a necessary ingredient. This didn't work as well as they hoped, because it turns out that uranium is much more plentiful than they had realized; the only reason nobody knew this is because prior to the atomic bomb, there weren't really good reasons to look for uranium deposits.

The other, public approach to this was by pursuing a treaty at the newly-created United Nations that would cover what was called "the international control of atomic energy." This basically would mean, a treaty that would ban the production of nuclear weapons, and be a treaty you could have some faith in. So it would involve verifying that people were in fact abiding by the treaty, and this would be done by monitoring the types of facilities that would transform the uranium ore already mentioned into the kinds of products (enriched uranium and plutonium) that could be used as bomb fuel. This approach was very much against secrecy — it was about how transparency could lead to security — and focused on the most tangible and easily-monitorable aspects of making atomic bombs, namely the massive factories and buildings that produced their fuel.

A proposal to this effect, called the Baruch Plan, was proposed to the United Nations in 1946. The Soviet Union, however, rejected it: the inspections measures, they argued, were too intrusive (it would allow the US/UN to see military/state secrets that were not atomic), and they strongly objected to the fact that under this plan, the US would keep its atomic stockpile until it was verified that no other country was building bombs, and only then would they dismantle theirs (or hand them over to the UN). (You might wonder: Why would the US even offer to give up its nukes? Because if it didn't, few others would even for a moment think about signing such a treaty.) So the treaty was dead in the water, and further discussions didn't result in anything workable, and it later became clear that one of the many reasons the Soviets didn't agree to it is because they were building their own atomic bomb as fast as they could, because they didn't trust the US and didn't want to be vulnerable.

The Soviets also, it turned out, had access to espionage information from the Manhattan Project, which points again to the ineffectualness of secrecy: spies exist, and will probably figure out what you don't want them to.

You then ask, why didn't the US do anything if others "stole" it? The answer is: what do you expect them to do? Wage a third World War, something that was unpalatable even before atomic bombs, but potentially suicidal (to you or your allies) with them? The military options were very limited, even in the brief period when the US had a monopoly on atomic bombs.

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