As the Cold War ended in the late 1980s and early ’90s, a new fear arose amid the rejoicing and relief: that atomic security might fail in the disintegrating Soviet Union, allowing its huge stockpile of nuclear warheads to fall into unfriendly hands. The jitters intensified in late 1991, as Moscow announced plans to store thousands of weapons from missiles and bombers in what experts viewed as decrepit bunkers, policed by impoverished guards of dubious reliability. Many officials and scientists worried. Few knew what to do. That is when Thomas L. Neff, a physicist at the Massachusetts Institute of Technology,...