An international team of nuclear physicists has found strong evidence for the existence of nuclear supersymmetry, a theory that relates bosons, which have integer values of spin, and fermions, with half-integer values of spin. The researchers from Germany, Switzerland and the US obtained the results in a series of complex experiments at the Paul Scherrer Institute in Switzerland, the University of Bonn and Ludwig-Maximilians University in Munich (A Metz et al. 1999 Phys. Rev. Lett. 83 1542). The findings are the culmination of sustained effort by many people to establish the validity of theoretical ideas that link the properties of various nuclei. This relation follows from a “supersymmetric” transformation that converts bosons into fermions and vice versa.

At the quantum level, bosons and fermions behave differently: bosons are sociable and do not object to sharing the same quantum numbers; fermions, on the other hand, shy away from each other because the Pauli exclusion principle forbids them from occupying the same quantum state.

One of the major breakthroughs in physics this century has been the development of theories that treat bosons and fermions on an equal footing. Thus each elementary boson has a much heavier supersymmetric partner that is a fermion and vice versa. The photon has a massive partner called the “photino”, for instance, while each quark is partnered by a corresponding “squark” and so on. Currently there is no evidence for supersymmetric particles, despite dedicated searches at the world’s high-energy particle accelerators. Meanwhile the holy grail of such supersymmetric theories is the unification of all the forces in nature.

Nuclear physics, which aims to describe the atomic nucleus in terms of its constituent neutrons and protons, also has its supersymmetric theory. The mathematical theory behind this is the same as in elementary particle physics. While the physics of nuclear supersymmetry is somewhat more mundane than the high-energy version, it has, on the other hand, already been subjected to direct experimental verification.

In the standard portrayal of the nucleus, known as the nuclear shell model, the core of the atom is described in terms of a collection of interacting nucleons (i.e. neutrons and protons) all of which are fermions. Since tens, even hundreds of nucleons may be involved, this description can be complex and there is no exact solution that can account for all of the properties of such a nucleus. Fortunately, the nuclear interaction encourages identical nucleons to pair up (i.e. protons with protons and neutrons with neutrons) so that they behave like bosons that can then be treated as nuclear building blocks. The first model of the nucleus in terms of interacting bosons was proposed in 1975 by Akito Arima, then at the University of Tokyo (and now minister for education in Japan), and Francesco Iachello from Yale University in the US.

In 1980 Iachello realized that supersymmetric theory could also be applied to nuclei because of the simultaneous occurrence of fermions and bosons, albeit effective bosons made from pairs of fermions. In practice, a nucleus containing an even number of protons and neutrons (an even-even nucleus) could be linked to a nucleus comprising an even number of protons and an odd number of neutrons (even-odd) or one with an odd number of protons and an even number of neutrons (odd-even).

Iachello’s suggestion prompted frantic activity as experimental teams around the world sought to verify the validity of the conjectured relation between nuclei that previously had been thought to behave very differently. And several pairs of nuclei – such as osmium-190 (even-even) and iridium-191 (odd-even), and platinum-194 (even-even) and platinum-195 (even-odd) – were indeed found to obey the relations proposed by Iachello. Later several experimental teams found more supersymmetric pairs of nuclei, providing firm evidence for this aspect of nuclear supersymmetry. In all these examples, the nuclei in each pair differed from one another by either a single proton or a neutron. There was, however, one piece missing from this nuclear supersymmetric jigsaw. It should be possible to further transform both an odd-even nucleus and an even-odd nucleus into one with odd numbers of both protons and neutrons.

In 1985 Vladimir Paar and co-workers from the University of Zagreb in the former Yugoslavia proposed that odd-odd nuclei could be described in terms of bosons plus one neutron and one proton. Shortly afterwards Jan Jolie, Kris Heyde and the current author (then at the University of Gent in Belgium) and Alejandro Frank from the Universidad Nacional Autónoma in Mexico interpreted this finding in the context of a nuclear supersymmetric scheme. We proposed that the properties of quartets of nuclei could be linked by supersymmetry – a conclusion that was also reached by Iachello and Baha Balantekin at Yale. Although the proposed theoretical formalism of “quartet supersymmetry” was elegant, there was scant experimental evidence for it. In particular, data were lacking on the fourth, odd-odd member of the proposed quartets. Over the years more information was gathered concerning these odd-odd nuclei, most notably by Michel Vergnes and co-workers at the Institute of Nuclear Physics at Orsay in France, but on the whole evidence for supersymmetry in quartets of nuclei remained dubious.

In 1991 Jan Jolie from the University of Fribourg in Switzerland set up a research programme to investigate the problem in detail. In recent years he has led several research teams and used a range of different nuclear reactions to painstakingly map out the energy spectrum of gold-196 (an odd-odd nucleus). Its spectrum can be predicted by applying supersymmetric transformations to the previously well measured energy spectra of platinum-194 and gold-195, and the energy spectrum of platinum-195, which was remeasured in the course of this investigation (see figure).

For example, in one of the reported experiments gold-197 nuclei were bombarded with polarized deuterons, bound states of one proton and one neutron. A particular reaction involved the deuteron picking up a neutron, hence transmuting the target nucleus into an excited state of gold-196. Jolie and co-workers measured the energy and scattering angle of an outgoing triton (a nucleus with one proton and two neutrons) and studied the decay of gold-196 as it emitted gamma rays in order to learn about its excited states. The researchers also studied other reactions involving different combinations of projectile and target nuclei at several energies to crosscheck the results. The team established several new energy levels in the gold-196 spectrum due to the improved energy resolution of their gamma-ray detector compared with earlier experiments.

The revised energy spectrum now agrees with the supersymmetry prediction based on a fit to the energy spectra of the three other nuclei in the quartet, and thus vindicates the theory. The search is now on for more examples of nuclear quartets to try and acquire a microscopic understanding of nuclear supersymmetry in terms of nucleon-nucleon interactions.