Would an Atomic Blast Stop the Oil leak?

It doesnt have to be nuclear, a conventional-explosive version could be engineered that would have the same effect. You arent trying to level the industrial capability of a city, you're just trying to plug one pipe :)

A large, high-temperature thermal charge (ie, something like magnesium or thermite) might even be enough to melt the pipe and surrounding rock enough to seal the leak.

Possibly, and in fact it's even possible that is being quietly contemplated since we are drilling two relief wells next to the leaking well. However, and it's a big however, there are some problems with this that make it problematic:

The Russian attempts, which were successful four out of five times, were all in above ground wells. We don't understand the geology of the area of the leak as well as the Russians did, so placing the charge properly would be tricky.

This area contains methyl hydrate deposits, they aren't mapped out, and we don't know what the pressure wave from a nuclear blast might do to them.

The Russians have a lot of experience with this technology and even had custom bombs built for this purpose. The USA has nothing of the kind, and it's a very good bet that the Russians won't be sharing any of their expertise with us. For one thing it's highly classified, for another if they did help us and it went sour, they would get blamed.

Nope, this is last ditch desperate solution. If the relief wells fail, they may attempt it. Let's hope not, because it could conceivably make the situation worse.

If someone suggested this as a viable option without having researched the geology/lithology of the test Russian blasts and contrasting them to the gulf..for at least 6 months, then I would like to see them committed to a home for the criminally insane!

The chances of this actually helping might be about 30% if all the proper research was done, however there would be a 70% chance of causing a literally unstoppable blowout , from several zones and of several fluid types that would literally flow forever. A person who would catually give this one the nod would have to be considered a homicidal maniac!!

Explosions stimulate oil and gas production, they don't cause flow to stop or wells to magically seal themselves!!!

There is no guarantee on it stopping the leak, but the oil will be radioactive after the nuclear detonation

Its a perfectly viable solution. the oil wouldnt now be radioactive as you guys said, its hitting rock miles underground, the rock itself is unimportant and is not a hazard in anyway.

People are far to afraid of radiation for some reason. it cant get through a mile of rock

okay, proactive thinking i guess. but then what do we do about the radiation that is in the gulf of mexico? That would make matters crappy in a different way.

No, it would make the hole bigger, and the entire Gulf would become radioactive.