Boson quasispin in the generalised Bohr-Mottelson model

Abstract

It is shown that the GBMM (an outgrowth of the Bohr-Mottelson model to encompass isovector vibrations) is endowed with an Sp(20, R) algebraic structure. This is connected with the fact that independent proton and neutron harmonic oscillations, which are described by U(10), are the main part of this model. The interaction between the different vibrations are described by the non-compact generators of Sp(20, R). A mathematically rigorous statement (complementary to the geometrical formulation) of this new symplectic model is presented. The algebraic setting of GBMM enabled us to introduce in a natural way a discrete boson variable, B-spin, which classifies the states according to their d- z (isoscalar-isovector) symmetry character. By using group-theoretic and recursive techniques we have explicitly constructed a basis associated with the group chain U(10) ⊃ N SU d+z (5)⊗ (B, B 0 SU B(2)⊃ SO d+z L ⊃ SO d+z L 0 (2) This basis is indispensable for future applications of GBMM. Finally, we compare the F-spin (IBM-2) and B-spin (GBMM) concepts.