I think that the fear of nuclear weapons' use converged with the fear prompted in the Cold War. Leading into the ending of the Second World War, there was a healthy amount of distrust between both sides. The dropping of the bomb on Hiroshima and Nagasaki helped to further this divide even more because of the latent fears and opposition already present. The underlying element of the Cold War became the use of the bomb by either side and how growing tensions between the two could trigger its use. In the end, this became the issue that existed between Communist Russia and the Capitalist West. I think it would make sense to be able to advocate that the spread of Communism and the containment policy of the West towards it was driven by the fear of nuclear weapon use by either side.
Your question is not very clear (I do not know what you mean by "a related text"), but I think that you are almost correct.
The main thing that is wrong with your statement is that communism does not spread after the Cold War. Communism spread at the very beginning of the Cold War and during the Cold War itself. Since the Cold War has ended, no new communist countries have appeared.
The Cold War pretty much starts "after the bomb" -- after the atomic attacks on Japan end the war. So in that sense, communism is related to after bomb.
Communism became a worldwide phenomenon in the late 19th century. Anyone interested in philosophy during this period took a long, hard look at the idealism of communism. In the early 20th century, communist powers took control of Russia and surrounding countries (changing the name to the Soviet Union). China and Cuba were taken over by communist factions afterwords. In the middle to late 20th century, communist nations were aiding communist factions in taking over countries such as Korea, Veitnam, Afghanistan, the Balkans, and some other places. This was viewed as a threat to the nations of the West.
The Cold War is a concept referring to the building of two nations with large-scale nuclear capability. The Unitied States stated that communism is evil. Communism is, by nature, anti-capitalist. This is where the bad blood starts. At its heart, communism is a system that is supposed to help the common people that capitalism theoretically alienates. In a capitalist society, there is a percentage of people who have most of the moeny; communism was supposed to rectify that. However, the leaders that arose in communist nations seemed to use the ideals of communism to rally support for their more selfish motives.
For those who did not live during the time of The Cold War, it can be equated somewhat to the way that people in the United States look at Muslims as being dangerous. There are some bad people associated with the Muslim faith, taking its tenets a bit too far. The difference, though, is that there were a couple of very large nations with governments possessing large armies that were seen as "the bad guys" instead of small radical groups. It was a frightening time, a time in which everyone thought the world could end at any moment.
I hope this helps with your question.