Remembrances of Dirac

In his fascinating article (Physics Today, November 2009, page 46 ), Graham Farmelo mentions Paul Dirac’s training as an engineer and the effect it had on his thinking. But the article barely touches on one of Dirac’s little-known practical accomplishments. Farmelo mentions that during World War II Dirac spent “part of the time developing an idea he had conceived for separating isotopes using an apparatus with no moving parts.” In fact, Dirac developed the fundamental theory of separation processes that underlies the design and analysis of today’s uranium enrichment plants, which provide fuel for almost all of the world’s nuclear power plants.

Dirac introduced the central concepts of separative work, which measures the effort needed to effect a prescribed separation. It is based on assigning to each isotopic concentration x a value V(x) = (2x − 1)ln(x/(1 − x)), the derivation of which involved a bit of Dirac magic. The results can be counterintuitive for the uninitiated. For example, it takes much less separative work to extract bomb-grade uranium (say, 90% ²³⁵U) from a batch of low enriched uranium, such as that typically used for power reactor fuel (say, 5% ²³⁵U), than it does to extract that amount of low enriched uranium from natural uranium (0.7% ²³⁵U). Physicists accustomed to associating Dirac with an ethereal approach to quantum electrodynamics may find it difficult to imagine him setting the theoretical foundation for an important industrial process. But he did.