Critical Mass Explained

To the Editors:

Several readers have suggested that I amplify my remarks concerning the critical mass of an atomic bomb in my article “Megaton Man” [NYR, May 23]. The New York Review has received the following text from the physicist Jeremy Bernstein, which seems to me useful in clarifying the processes involved, and which is published with Mr. Bernstein’s permission.

1. The critical mass—or better the critical size from which the mass can be computed—is determined by a competition between escape of neutrons from the surface of the fissionable material and creation of neutrons in the interior during the fission process. When this competition is a “draw”—as many neutrons are created as escape—you have reached the critical size. At Los Alamos it was necessary to find the critical mass of nonspherical volumes, which was done by adding more pieces of fissionable material until the critical mass was reached. One version of this was referred to by Richard Feynman as “tickling the dragon’s tail,” and it was so delicate that the people who added the last masses had to jump off the top of the assembly of fissionable material to avoid acting like tampers and reflecting neutrons back into the material.

2. When the actual critical mass is reached nothing happens, so that to produce a nuclear explosion you need several critical masses—about three. In that case more neutrons will be produced in the interior than will leak through the surface; as a result a self-sustaining chain reaction will occur. This poses an apparent dilemma. How do you assemble several critical masses if you start with an amount of material that is less than a critical mass, which you must do to avoid pre-detonation? The secret has to do with the density of the material. What you call the critical mass depends on the density. If you increase the density, the critical mass becomes dramatically smaller. If, for example, you increase the density by a factor of two, the critical mass is decreased by q factor of four. In a bomb what happens is that the material is rapidly compressed so that this compressed material has a smaller critical mass and hence you can achieve several critical masses at these compressed densities.

Alan Lightman
Concord, Massachusetts