Part of the military contribution just mentioned :
The Making of the Atomic Bomb, by Richard Rhodes (Winner of the 1987 National Book Award) (HC, 1986, 886 pages, $4)
Atomic Audit: The Costs and Consequences of U.S. Nuclear Weapons since 1940, edited by Stephen I. Schwartz (SC, 1998, 680 pages, $3)
Peace is a Three-Edged Sword, by Lloyd Mallan (HC, 1964, ex-lib, $1)
'It was 5 a.m.... Suddenly lights on a signal board indicated that something had gone wrong with... the two giant radar stations designed to detect enemy missiles high across the Arctic wastes... For slightly more than four minutes war seemed possible. Then... communications ... were resumed." The author writes this book to show that the checks and counter checks "make it all but impossible for a full-scale war to be started by accident, madness or hysteria".
(Oh, really?)
Morality and the Bomb: An Ethical Assessment of Nuclear Deterrence, by David Fisher (HC, 1985, 136 pages, $1)
The Dead Hand: The Untold Story of the Cold War Arms Race and It's Dangerous Legacy, by David E. Hoffman (HC, 2009, 575 pages,$2)
"The suspense filled story of the people who sought to brake the speeding locomotive of the arms race, then rushed to secure the nuclear and biological weapons left behind by the collapse of the Soviet Union."
Look for these books in the military history section.