Nuclear theory gets analytical
Jun 1, 2001
Phase transitions have fascinated physicists for centuries. The formation of ice is an everyday example of a material that changes shape at a phase transition, while more exotic examples are found in nuclear and particle physics. But describing the detailed properties of nuclei in the phase-transition region has previously eluded theorists. Now Franco Iachello of Yale University in the US has developed an analytical model that predicts various nuclear properties, including the energy levels and transition rates, for any nucleus undergoing a certain phase transition. The theory has been boosted by the discovery by Rick Casten and Victor Zamfir, also at Yale, of nuclei that match the predictions (F Iachello 2001 Phys. Rev. Lett. 87 052502; R Casten and N Zamfir 2001 Phys. Rev. Lett. 87 052503).
Phase transitions in nuclei are difficult to understand because of the many degrees of freedom involved, so theorists have had to rely on complex numerical calculations that contain many free parameters. To understand these nuclei fully, however, physicists need a mathematical model that can describe their different properties without a large number of guiding assumptions. Iachello has now developed such a model - which he calls X(5) symmetry - for spherical nuclei that transform into a rugby-ball shape during a phase transition. By solving the Schrodinger equation at the critical point - the point where both states co-exist - he can predict the properties of phase-transition nuclei by simply plugging in their quantum numbers. The theory could also be applied to metallic clusters, molecules and polymers.
By chance, recent experiments at Yale, Cologne University in Germany and the Institute Laue-Langevin in Grenoble, France, hinted that samarium-152 nuclei undergo exactly the right type of phase transition. With 62 protons and 90 neutrons, these stable nuclei were thought to lie close to the critical point. Casten and Zamfir have now taken a closer look at the energy levels of excited samarium-152 nuclei, and the strengths of the transitions between them. In general, they found an excellent agreement between the measurements and X(5) symmetry. They also found that neodynium-150, like samarium-152, co-exists as spherical and rugby-ball nuclei.
"This is one of the most interesting things I have ever done," Casten told PhysicsWeb. X(5) symmetry gives experimentalists a new benchmark against which to test nuclei. With the production of ever more exotic nuclei at radioactive beam facilities, Casten believes that the latest work has a good chance of "starting a new direction in nuclear physics".