The Microscopic Interacting Boson Model for Identical Nucleon Systems.

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 S-D states, are appropriate to describe low energy quadrupole collectivity in the nondegenerate multishell case. The properties of the S-D 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 S-D states are found to have a property called kinematical particle-hole equivalence, which means that any S-D state can be represented in terms of nucleon particle pairs or nucleon hole pairs. To fully specify the S-D 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 one-body potential and the two-body interaction terms of the fermion Hamiltonian play important parts in determining the IBM Hamiltonian.