An Intrinsic State with Definite Isospin for IBM-3

Abstract

No doubt Francesco Iachello, like the Prince in “The Leopard”, has found consolation in his many contributions to physics. One of his original contributions is the interacting boson model1 (IBM-1). The model, based on interacting monopole and quadrupole bosons, was initially interpreted as a quantization of the Bohr-Mottelson quadrupole liquid drop model. Later a distinction was made between neutron and proton bosons2 (IBM-2). These bosons were interpreted as correlated monopole and quadrupole pairs of neutrons and pairs of protons, a generalization of the pairing model which was restricted to monopole correlated pairs only. This paved the way for a microscopic interpretation of the boson model by establishing its link with the nuclear shell model. The IBM-1 states were shown to correspond to the subset of states of IBM-2 which are completely symmetric in the neutron and proton degrees of freedom and belong to the highest representation of the F-spin group3. The latter is an SU(2) group which classifies the states of IBM-2 according to their symmetry properties with respect to a rotation of neutron bosons into proton bosons and vice versa. The connection of both IBM-1 and IBM-2 to the Bohr-Mottelson-like quadrupole deformations is made by introducing an intrinsic state4-7 for the boson system. With this intrinsic state, collective motion in the IBM can then be given a geometrical visualization in terms of quadrupole deformation parameters.