Abstract

In the interacting boson-fermion model for odd nuclei it is shown that mixed- symmetry boson states may occur at low excitation when neutrons and protons occupy the same shell-model orbits. In any of the forms of the interacting boson model (l, 21 IBM~, -3 or -4 in which there is more than one type of boson, it is possible to have states which are less than fully symmetric in the separate orbital and intrinsic spaces. Such states are said to be of mixed symmetry and are labelled by a partition of the boson number N. Calculations for even-even nuclei show that low-lying states are dominated by full symmetry and that the lowest states of mixed symmetry have the partition (N- 1, 11. These states of mixed symmetry have been identified experimentally, mainly through their Ml properties, and examples are the I+ states (3) at 3.08 MeV excitation in lshGd and the 2+ state (4) at 1.99 MeV in 14Ba. The boson model (5) for an odd nucleus (IBFM) consists of a single nucleon coupled to the boson structure for the even-mass core. In the IBM~ version of the model, which is appropriate for heavy nuclei with valence neutrons and protons in different orbits, each nucleus has a unique assignment of neutron and proton boson numbers N, and N, and a unique charge for the single nucleon. In this situation the states of the odd nucleus in which the bosons have mixed symmetry would be expected to lie at about the same excitation as in even-even nuclei (see above). However, in lighter nuclei, with valence neutrons and protons filling the same orbits, it is necessary to extend the boson model to IBM~ by introducing a third type of boson composed of a neutron and a proton in order to preserve isospin symmetry. Odd nuclei may also be described (6) in this region (IBFM~) but the single nucleon must now be vector coupled, in isospin, to the bosons. This implies that, in an odd-neutron nucleus, for example, the single nucleon spends part of its time as a neutron with an even-even boson core and part of its time as a proton with an odd-odd boson core. The question of the excitation energy of the mixed-symmetry states in the odd nuclei is then a more delicate one. Here we explore that question and show that in certain odd nuclei the mixed-symmetry states are at lower excitation than in the even-even nuclei. Consider a nucleus with an odd number n of nucleons beyond a double closed shell such as 40Ca or 56NNi. The number of bosons is then N= f(n - 1) and we shall discuss states with full symmetry (NI and with the lowest mixed symmetry (N- 1, 11. The possible total isospin may take the values T=tn, 3n- 1, in-2, . . ., and, from

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