The opening up of Soviet archives after the end of the Cold War indicated that, contrary to a lot of US sentiment at the time, Stalin had no interest in an ongoing, expansionist war with anyone, much less the United States, in the early Cold War. Did the atomic bombs play a role in that? It's obviously hard to say, since the bombs did exist. But there is a lot of reason to think that the Soviets had, by the end of WWII, tired of that kind of war anyway, and were not so stupid to think that they could just roll over their Western Allies without a lot of trouble and putting themselves in a lot of risk.

That does not mean that the Soviets were not willing to play various kinds of near-war scenarios. The Berlin Airlift was an attempt to gain West Berlin by fiat, the Korean War was (we now know) something he agreed to with some reluctance to help the North Koreans, and did not think it would spiral into something larger. It seems fairly clear that the Soviets were aware that the US would not eagerly rush into a new, full-scale war, atomic or otherwise, and they did many things that probed the boundary of the US willingness to engage in conflict. They were determined, to some degree, to avoid being "intimidated" by the atomic bomb — they were very self-conscious about making it appear that they did not care about it, though in secret we know Stalin had instructed his scientists to develop one for him as soon as could be done, the highest priority, to avoid the possibility of the USSR becoming another Japan.

Did the bomb impact their overall policy, and if so, how much? It's really not clear. It's worth keeping in mind that the US nuclear arsenal was, until about 1950, very small and very hard to deploy. Until the Soviets themselves got the bomb, the US was essentially still in a World War II capability with regards to nuclear weapons. They could not knock the USSR out of the fight in one fell swoop, and they had to have bombers launched from forward bases relatively near their targets (and hope they weren't shot down). The weapons themselves were still complex and not entirely reliable. Their destructive power was, by later standards, modest. Which is only to say: the atomic bomb would be a force in a true US-Soviet war, but there would still be a lot of room for conventional fighting. It would be a drawn-out conflict on both sides.

It's hard to disentangle the bomb from everything else. It is easy to claim, in a blanket way, that the bomb must have affected Soviet willingness for war, without anything to point to to support it. (Especially if you imagine, as many Cold Warriors on the US side did, that Stalin had an infinite desire for expansion, which, again, does not seem to be exactly true.) Maybe it did, maybe it didn't — this is an immense counterfactual, and there is plenty of room for disagreement. It depends, in part, on how much "power" you ascribe to the atomic bomb, and while today we tend to imagine that it was always seen with an awe that we give nuclear weapons today, in the 1940s it was not uncommon for major military and world leaders to express that they thought it was overblown. And it is worth keeping in mind, again, that the advent of thermonuclear weapons on long-range missiles did not occur until the 1950s and 1960s, and that, by itself, dramatically changed the character of what a nuclear war would look like. It is important not to superimpose a 1960s attitude towards nuclear weapons onto people in the late 1940s — some people regarded the weapons like that, but many did not.

John Lewis Gaddis, The Cold War: A New History and We Now Know: Rethinking the Cold War are worthwhile reads if you are interested in these sorts of questions, as he synthesizes what is known from new sources very well into the older narratives and assumptions.

Hi there -- while there's always more to be said on the topic of whether the bombs were intended to intimidate the USSR, you may also be interested in this section of our FAQ on the atomic bombings.