Subatomic Physics

18.6. The Interacting Boson Model 563
Figure 18.14: Energy spectra of even–even Os isotopes. The theoretical (th) rotational bands
(GSB) and vibrational bands (γ-band) based on the ground state are compared to experiment
(ex). [From W.-T. Chou, Wm. C. Harris, and O. Scholten, Phys. Rev. C37, 2834 (1988).]
to Cooper pairs (32) in superconductivity and it has been possible to use the tools
and ideas developed to explain superconductivity (33) in nuclear physics. Arima and
Iachello also take into account the somewhat weaker attraction for nucleons in a
relative d-state. This inclusion can be related to the shell model and to the concept
of seniority introduced by Racah. (34) In this scheme nucleons tend to pair to spin
zero (seniority 0) and the next most likely pairing is to spin 2 (seniority 1).
In the IBM the paired particles in s- andd-states are treated as bosons and the
bosonic degrees of freedom are able to describe well the spectra of even–even nuclei
without invoking shape variables. The emphasis is on the dynamics of the bosons
rather than on the shape variables of the collective model. Further, by incorporating
s-bosons as well as d-bosons there are six degree of freedom to be compared to the
five degrees of the collective model, represented by α2m of Eq. (18.36). These
features differentiate between the IBM and the collective models. By introducing
also unpaired fermions, the model has been extended to odd–even nuclei. Thus, the
IBM treats collective and pairing degrees of freedom on the same footing.
A state is described by fixed numbers of s-bosons (ns) andd-bosons (nd); the
total number of bosons is N = ns + nd. In the more recent model, IBM2, neutron
pairs and proton pairs are treated separately. For either neutrons or protons, the
Hamiltonian thus consists of the kinetic energies of the bosons in s- andindstates
and the interactions between them. The connection to the collective model
is obtained by considering the classical limit. A coherent state with ns s- and
32 L. N. Cooper, Phys. Rev. 104, 1189 (1956).
33 J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
34 G. Racah, Phys. Rev. 63, 367 (1943); 76, 1352 (1949).