Microscopic interacting boson model for identical nucleon systems

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:5004703

Johnson, A B

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 nontrival 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. The author introduces 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. The author finds 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. The author presents and applies 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.

• Research Organization: Pittsburgh Univ., PA (USA)
• OSTI ID: 5004703
• Country of Publication: United States
• Language: English

Related Subjects

653001* -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
653007 -- Nuclear Theory-- Nuclear Models-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CONFIGURATION MIXING
ENERGY LEVELS
HAMILTONIANS
INTERACTING BOSON MODEL
INTERACTIONS
INTERMEDIATE MASS NUCLEI
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
NUCLEAR MODELS
NUCLEI
QUANTUM OPERATORS
S STATES
SHELL MODELS