Synopsis: Spin doctoring the Dirac equation

The Dirac and Klein-Gordon equations provide a full relativistic description for particles with spin ½ and 0, respectively. A calculation now shows how to extend this description to particles, such as nuclei, with spin greater than ½.
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Writing in Physical Review A, Krzysztof Pachucki of the University of Warsaw reports progress on a fundamental problem that goes back to the early days of quantum mechanics. All physics students learn that the Dirac equation provides the natural description of fermions with spin 1/2, such as the electron. By combining the special theory of relativity with the Schrödinger equation, Paul Dirac in 1928 obtained a remarkable new equation that predicts both the existence of anti-matter (positrons), and a g-factor of 2 for the magnetic moment of the electron – i.e. the magnetic moment is twice what one would expect if the electron spin were treated as a classical current loop.

The Klein-Gordon equation provides the natural description for relativistic particles of spin 0 (suitably interpreted), but surprisingly, there is no similarly well established and unique equation for particles, such as many atomic nuclei, that have spin 1, 3/2 and so on. For example, corrections for the recoil motion of the nucleus in an atomic system require a proper relativistic theory analogous to the Dirac equation for particles with spin greater than 1/2. Now, Pachucki has solved the problem, at least in part, by identifying the mathematical terms that are necessary to do the full relativistic calculation and construct the right interaction Hamiltonian.

The result extends the state-of-the-art for what we can calculate at the fascinating interface between atomic and nuclear physics, and opens the way to new high-precision measurements that can be interpreted in terms of fundamental properties of the nucleus. - Gordon Drake


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