Quartets of superdeformed bands and supersymmetry breaking

We examine the prediction of supersymmetric quantum mechanics that bands with identical gamma-ray energies occur in quartets. The experimental data suggest that this scenario is actually realized in nature. In the $A=150$ mass region, four known pairs of isospectral bands can be grouped in two quartets, while there are indications of such patterns around $A=190$. We introduce a small supersymmetry breaking, necessary to describe the details of the data. We derive relations among the transition rates that can be used to test our predictions. pacs: 21.10.Re, 11.30.Pb, 21.60.Fw, 23.20.Lv