J. Phys. G : Nucl. Phys. 9 (1983) 521-534. Printed in Great Britain Rotational limit of the interacting two-vector-boson model A Georgieva, P Raychev and R Roussev Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, Sofia, Bulgaria Received 13 September 1982, in final form 31 December 1982 Abstract. The rotational limit of the interacting two-vector-boson model (IVBM) is investigated. This limit arises if the Hamiltonian is ‘pseudospin’ invariant and corresponds to the following reduction chain of subgroups: U(6)3 U(3)$U(2)30(3). Analytic relations for the energies and E2 transition probabilities within the ground-state band, the p and y vibrational bands and between the vibrational bands for the strongly deformed even-even nuclei are obtained. 1. Introduction Recently (Georgieva et a1 1981, 1982) an interacting vector-boson model (IVBM) has been proposed for the description of the collective nuclear properties. In the IVBM the collective motions in nuclei are described in terms of two types of vector bosons (angular momentum L = l), differing in the projection To of an additionally introduced quantum number T, called a ‘pseudospin’. It turns out that within the boson space the most general one- and two-body Hamiltonians can be expressed in terms of the generators of the symplectic group Sp( 12, R). This means that the eigenvectors of the Hamiltonian form the basis of a unitary irreducible representation (UIR) of Sp( 12, R). On the other hand, the Hamiltonian must be invariant only with respect to the rotational group O(3) generated by the angular momentum operators. On that account the Hamiltonian reduces the Sp(12, R) symmetry to 0(3), i.e. Sp(12,R) is a group of dynamical symmetry in the sense of Dashen and Gell-Mann (1965). In the first stage of the development of the model we assume (Georgieva et a1 1982) that the Hamiltonian H should preserve the number of bosons. In this case H can be expressed only in terms of the generators of the maximal compact subgroup of Sp( 12 R), namely the group U(6). In fact that assumption means that the mixing of the different U(6) multiplets belonging to a given UIR of Sp( 12, R) is neglected. This approximation seems to be sensible for the description of the low-lying collective states in nuclei. The dynamical group U(6) necessarily includes the rotational group O(3) and in order to classify the states it is necessary to determine the different chains of subgroups, which reduce the U(6) symmetry to O(3). It has been shown by Georgieva et aZ(l982) that the a 1983 The Institute of Physics 521