Bulg. J. Phys. vol.48 no.5-6 (2021), pp. 457-466



A Symmetry Connecting the Shell, Collective and Cluster Models

J. Cseh
Institute for Nuclear Research, Debrecen, Bem ter 18/C, Hungary-4026
Abstract. The relation of the fundamental structure models is discussed. Their common intersection is provided by the U(3) dynamical symmetry for the single shell problem, and by the multiconfigurational dynamical symmetry (MUSY) of group structure Us(3) ⊗ Ue(3) ⊃ U(3) ⊃ SU(3) ⊃ SO(3) for the major-shell-excitation. Both of them show dual breaking: U(3) and SU(3) of the total Hamiltonian are dynamically broken, while SO(3) of the intrinsic Hamiltonian is spontaneously broken, resulting in deformed shape. MUSY has a composite nature: a simple dynamical symmetry is present in each configuration, and a further symmetry transforms them into each other. Together with the antisymmetrization it can completely wash out the difference between the model pictures, thus occasionally cluster and shell wavefunctions can be identical.

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