Also, it is unlikely anyone would have realistically expected uranium to be delivered to Japan by U-boat in 1945.
Not exactly, although they contributed a lot to the early work. If we start from "splitting the [heavy] atom", the first practical method, a German radiochemist was the first to recognize what happened, and the German physicist he first forwarded this information and her nephew figured out how it worked. But those two were Jews in exile, and most of the following more practical stuff was figured out, correctly at least, by scientists outside of Germany. Inside, they suffered a couple of disasters, a silly failure to get an higher priority for the project, and an incorrect evaluation of using graphite as a moderator, limiting them to heavy water. Which we made sure through sabotage that they couldn't get more/enough of.
But if you put on your alternate history cap, note Heisenberg and Himmer's relationship from when they were school kids, direct all the V-2 resources into the bomb, who knows? Many on both sides were legitimately worried the Germans would get the bomb in time.
As for the Japanese, no way. Besides what you read in the article, thermal diffusion was all but a failure in the US, among other things required fantastically too much steam, and was only revived to provide somewhat enriched feed stock into the caltrons (modified cyclotrons), and later into the gaseous diffusion plant before it fed the caltrons. ADDED (forgotten while drafting): centrifuges were of course obvious, and about the first thing we tried, but were beyond the state of the art then.
1,200 pounds of uranium at the normal 0.72% U-235 would not come close to yielding one critical mass, and for gun assembly apparently you need more like 3 times the normal pressure critical mass, although it doesn't all have to be of the highest grade.
On the other hand, with as far as I know no more info than the Germans had, Otto Frisch and Rudolf Peierls estimated in early 1940 that a kilogram of U-235 might do it, see https://en.wikipedia.org/wiki/Frisch%E2%80%93Peierls_memoran...
They pretty much laid out the correct physics mechanism (fast neutrons) and were only off by a factor of 15 on the amount required; pity for Adolph that they were Austrian and German Jews self-exiled in England by then.
But you're quite right. Heisenberg used an incredibly faulty method of calculating critical mass. And everyone around him simply deferred to his expertise. His method involved considering a branching tree of neutron chain reactions inside a sphere of fissile material, and if this tree can grow to include about 1 mole of material then that should be about enough to release enough energy for a "bomb". The reality is that it's completely unnecessary for an entire neutron chain-reaction tree to be encompassed within fissile material. All that matters is that on average from generation to generation there is a multiplication of neutrons, which will then grow geometrically incredibly rapidly. And that can happen even with many "branches" of the tree leaving the sphere and not contributing to future reactions.
In hindsight, he was actually blatantly incorrect. Dude knew it was possible and convinced the rest of the German scientists it wasn't, for long enough to make a difference. If you read between the lines, he's almost gloating in that transcript.
"On the other hand the whole heavy-water business, which I did everything
I could to further, cannot produce an explosive."
"We wouldn't have had *the moral courage* to recommend to the government
in the spring of 1942 that they should employ 120,000 men just for
building the thing up."
"The point is that the whole structure of the relationship between
the scientist and the state in Germany was such that although we
were not *100% anxious* to do it, on the other hand we were so
little trusted by the state that *even if we had wanted to do it*,
it would not have been easy to get it through."
"Well, that's not quite right. I would say that I was absolutely
convinced of the possibility of our making a uranium engine,
*but I never thought we would make a bomb, and at the bottom of
my heart I was really glad that it was to be an engine and not a
bomb. I must admit that*."
Reading "The Man Called Intrepid", I saw something I had never noticed before: Germany occupied Denmark and conquered Norway before the main thrust into France. If you think of that as acquiring Niels Bohr (Denmark) and a heavy water supply (Norway), it becomes much more frightening. (Was that what Germany was thinking? I have no idea. But it's what at least a few people in England were afraid Germany was thinking.)
"The candle that burns at both ends burns twice as brightly" is kind of a recurrent theme. Really the only way you wouldn't get that boiling-over that resulted in the Nazi takeover and the Holocaust would have been for the Treaty of Versailles to go way easier on them, or at least once the depression started happening. Once you fuck over a country with massive debt repayments within the context of a global depression, nationalistic backlash is inevitable. See: the current situation with Greece and the increasing rise of the fascist Golden Dawn party, who have been hovering disconcertingly close to double-digit territory lately.
And by that point in the alternate-universe hypothetical we're pretty much talking Kumbayah territory. By 1960 we've formed the one-earth government, we're on the moon and have eradicated polio. Nowadays we're probably vacationing on the moon, 10% of the world population lives on spaceships, and we've got an asteroid in orbit being strip-mined and outfitted into an Aldrin cycler for our Mars settlement.
Wait, why can't I live in that universe again? Not the one with Khan, the one with the asteroid mining...