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 state^4-7 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.

“During these moments of abstraction he seemed more intimately absolved, in the sense of being linked anew with the universe.”