APPLICATION AND DESCRIPTION OF THE INTERACTING BOSON MODEL

• Main Author: Duval, Philip Dewitt
• Other Authors: Barrett, Bruce R.
• Language: en_US
• Published: The University of Arizona. 1981
• Subjects: Bosons.; Quantum statistics.
• Online Access: http://hdl.handle.net/10150/281989

The Interacting Boson Model (IBM) of Arima and Iachello and co-workers is one of the most successful theories for describing the properties of the low-lying energy levels of medium-to-heavy mass nuclei. A review of the principles and phenomenology of the IBM is presented. The basic IBM is then applied to the even tungsten isotopes and compared with experimental observables associated with the low-lying states. These observable include transition rates, branching ratios, ρ(EO) values, quadrupole moments of the first two excited 2⁺ states, two-neutron separation energies, and isomer and isotope shifts. The results are seen to agree very well with the experimental data. Following the study of the tungsten isotopes an extension of the IBM to describe configuration mixing is presented. This extension is seen to be necessary when there are only a few valence protons or neutrons. In such cases the low-lying energy levels can be built upon more than one configuration. For example, states involving a two-particle-two-hole excitation from the core may occur in the same energy region as states made from only the valence nucleons. The extension of the IBM presented to handle such situations is quite general. A specific example using the light mercury isotopes and the molybdenum isotopes is given. The IBM is then examined from a microscopic point of view, using the generalized seniority scheme. The structure of the bosons of the IBM is given in terms of correlated fermion pairs. Predictions for the IBM parameters are obtained by constructing the zeroth-order image of the corresponding fermion operator. The predictions of a single j-shell approximation are compared with empirical results. In this approximation the valence nucleons are assumed to occupy a single j-shell whose effective j value is chosen so as to reproduce the total occupancy of the valence shell. Next, the predictions of a two non-degenerate j-shell approximation are compared with empirical results. This appoximation appears to be valid in both the 50-82 and the 82-126 neutron shells whose single-particle levels seem naturally to form two sub-shells. The predictions for the IBM parameters dependent on neutron number are seen to be in better agreement with empirically determined values than the predictions for the single j-shell (the proton-number dependent parameters are not treated). Furthermore, the two j-shell calculations reproduce the observed SU(3) or rotational character of the low-lying states of many mid-shell nuclides in the medium-to-heavy mass region. Finally, a brief description of the Interacting Boson-Fermion Model is given. This model is seen to be very successful in describing nuclei with an odd number of protons or neutrons. A calculation of the energy spectrum of the odd tungsten isotopes is presented.