Supersymmetry in nuclei

The concept of supersymmetry in nuclei has been extended in the last year to include the proton-neutron degree of freedom [HUB85,VAN85 ]. With this extension, it becomes possible now to predict prperties of odd-odd nuclei. Thus, in addition to providing the first experimental example of supersymmetry in physics [CAS84,1AC85], this concept appears now to be able to make predictions for yet unknown quantities. The experimental determination of the predicted spectra will indicate to what extent supersymmetry is useful in nuclear physics. 

Recent developments in applications of supersymmetry to the study of complex spectra are discussed. In particular, extensions of supersymmetry to nuclei with an odd number of protons and neutrons are presented. 

I wish to thank V. Paar, P. van Isacker, and A. Frank for pointing out the importance of supersymmetry in odd-odd nuclei and A.B. Balantekin and I. Bars for many discussions on the subject. This work was performed in part under DOE Contract No. DE-AC-02-76-ER-03074. 

The concept of dynamical supersymmetries was successfully used to connect the properties of even-even nuclei with the neighboring odd-even nuclei. If we want to study, say, the correlation between an even-even nucleus and the next, odd-proton nucleus, the first decomposition in the supergroup chain is... 

As an illustration of dynamical supersymmetry with canonical decomposition we construct a supermultiplet starting from the even-even nucleus 194Pt. In this region the proton shell is dominated by j = 3/2 and the neutron shell by j = 1/2,3/2,5/2. Hence n = 4 and n =12. The relevant representation of the appropriate supergroup U(6/16) is the one with Jf= 7. Various nuclei are placed in the tensor product representations as follows ... 

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