Was there a constant 'fear of the bomb' in the Soviet Union and America during the Cold War?

Or were there times where there wasn't such a fear? Possibly during the [Nixon-Brezhnev détente](https://en.wikipedia.org/wiki/Cold_War#Nixon.2C_Brezhnev.2C_and_d.C3.A9tente), or [Samantha Smith's](https://en.wikipedia.org/wiki/Samantha_Smith) peace activism?