The Microscopic Interacting Boson Model for Identical Nucleon Systems.
Abstract
The operators of the interacting boson model (IBM) are calculated by a microscopic method which extends the approach of Otsuka, Arima and Iachello (OAI). S and D pairs of nontrivial structure are used to construct a set of basis states which span a subspace of a general shell model space. These states, called SD states, are appropriate to describe low energy quadrupole collectivity in the nondegenerate multishell case. The properties of the SD states are similar enough to the properties of the IBM boson states that the OAI mapping procedure can be carried out and boson "images" of fermion operators obtained. The SD states are found to have a property called kinematical particlehole equivalence, which means that any SD state can be represented in terms of nucleon particle pairs or nucleon hole pairs. To fully specify the SD basis, an assumed prescription must be used to determine the structure of the S and D pairs. We introduce the concept of dynamical particle hole equivalence to describe a structure prescription that maintains the equivalence of particles and holes. Two structure prescriptions are applied and compared using a shell model space and an effective Hamiltonian appropriate for tin nuclei. We find that it is important to allow the D pair structure to vary with the nucleon number. The structure prescription MIN has dynamical particle hole equivalence. In order to determine the IBM Hamiltonian, matrix elements of the fermion Hamiltonian involving states with at worst two D pairs are evaluated. We present and apply a new method for evaluating these matrix elements, which are then used in obtaining the first calculation of the boson interaction for a system of identical fermions in the nondegenerate multishell case. We find that the boson interaction is strong and number dependent. Also, both the onebody potential and the twobody interaction terms of the fermion Hamiltonian play important parts in determining the IBM Hamiltonian.
 Publication:

Ph.D. Thesis
 Pub Date:
 1982
 Bibcode:
 1982PhDT........45J
 Keywords:

 Physics: Nuclear