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Dynamical Supersymmetries in Nuclei

F. Iachello

1980
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Physical Review Letters
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A similar picture was independently suggested by N. N. Nikolaev and S. Pokorski, Phys. Lett. 80B, 290 (1979); N. N. Nikolaev and A. Ya. Ostapchuck, CERN Report No. TH-2575 , 1978 . However, their model rests heavily on details of a specific quark recombination model, it is not applicable to lepton production, and their predictions involve a free choice of functions and adjustable parameters. We assume that quarks can propagate long distances through the nucleus as free quarks. We have not
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... . We have not addressed ourselves to the problem of what is the mechanism that makes this possible, whereas confinement distances are believed to be of the order of nucleon dimensions. The answer to this problem has to wait first for the solution of the confinement problem. It is well known both theoretically (see, for instance, Ref. 6 and references therein) and experimentally (lack of significant cascading within nuclei) that formation times of large x particles are long compared with nuclear dimensions. It is suggested that dynamical (Bose-Fermi) supersymmetries may be present in the spectra of complex nuclei. A concrete example in which a supersymmetric structure is experimentally observed is shown. In this example the supersymmetry is generated by I-= 0 and I. = 2 bosons together with j=2 fermions. In recent years, it has been pointed out by several authors that there may exist in nature examples of supersymmetric structures in which bosonic and fermionic degrees of freedom are linked together in a single theoretical framework. ' However, no concrete example in which a supersymmetric structure is experimentally observed has been reported so far. In this Letter, I suggest that dynamical supersymmetries may be present in complex nuclear spectra and I show one concrete example where the supersymmetric structure is experimentally observed. By analogy with an ordinary dynamical symmetry (which applies to a system either of bosons or of fermions separately), one can define a dynamical supersymmetry as that situation in which (i) the states of the combined system of bosons and fermions can be simultaneously classified with a complete set of group-theoretical labels; (ii) these states are split but not mixed by the Hamiltonian, H, and (iii) the same expression for the eigenvalues of the system in terms of the complete set of group-theoretical labels described both bosonic and fermionic spectra. The investigation of this problem was stimu-lated in part by the fact that similar attempts have been made in elementary-particle physics and in part by the known occurrence of several ordinary dynamical symmetries in the spectra of complex nuclei. ' In particular, the spectra of the platinum nuclei with an even number of protons and neutrons have been shown to display a dynamical symmetry associated with the group O(6). ' The states of these nuclei have then been classified by the set of labels related to the group chain~U (6) DO(6) 30(5) DO(3) DO(2), denoted by N, o, w, vz, L, and M. The group U(6) and its subgroups are generated by L = 0 and L = 2 bosons. In terms of these labels, the expectation value of the most general Hamiltonian which splits but does not mix the states can be written as'

doi:10.1103/physrevlett.44.772
fatcat:gsrkq37grfhzxlmnmo2b6nv76y