The G-Boson and Shell Model Mappings for the Interacting Boson Model

Couch, Andrew Stephen (1986) The G-Boson and Shell Model Mappings for the Interacting Boson Model. MSc(R) thesis, University of Glasgow.

Abstract

This Thesis embodies the work I conducted whilst at Glasgow University between Sept 1984 and July 1986. The project is an account of the current status of the Interacting Boson Model as applied to light nuclei, with an investigation into possible extensions of the current theory. The IBM has been well investigated phenonenologically , but the provision of a microscopic theory with relation to the spherical shell model is still to some extent illusive. Chapter 1 starts with a review of the general development of the model over the past decade, and then concentrates on two specific aspects of the model. The first is that of the IBM2, IBM3 and IBM4, in the SD shell. Here the results of other workers have been reproduced. The second topic is the g-boson. Chapter 2 considers and reviews some of the earlier boson expansion methods, which although conceived as particle-hole excitation mechanisms, are shown to give valuable information on general mapping procedures and microscopic pairing relations of fermions . Chapter 3 explains how a boson shell-model is constructed in the m-scheme, and the use of the Lanczos method discussing the relevant questions on convergence and fitting techniques. A new combinatorial procedure is described allowing the extension of current computer programs to include the g-boson (Glasgow-Lanczos-Morrison-Couch shell model code). A number of spectroscopic fits were carried out with various types of bosons in 24 Mg, which although not ruling out the sd-boson components in the low lying states, did indicate that a g-boson is a useful modelling tool in this region. Following this the work described in chapter 2 for the SD shell was extended to include a g-boson in a weak coupling limit. Other than producing the low lying 4+ state in 20O known to have a large g-boson component, it produced little effect on the low lying spectra of other nuclei in the SD shell. It was concluded here, that the g-boson if introduced with sd-bosons should be placed in a stronger coupled calculation. In the spirit of renormalised interactions, a second calculation was performed, in which the g-boson alone was used. Here, at least for the more deformed nuclei, the best agreement with experiment to date was obtained, although the overbinding of the IBM2 increased by 50 %. Chapter 4 presents the existing mapping procedures used in the IBM, and discusses two new approaches to this problem. A final section presents the general conclusions reached in the main Thesis.

• Item Type: Thesis (MSc(R))
• Qualification Level: Masters
• Keywords: High energy physics
• Date of Award: 1986
• Depositing User: Enlighten Team
• Unique ID: glathesis:1986-77473
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jan 2020 09:07
• Last Modified: 14 Jan 2020 09:07
• URI: https://theses.gla.ac.uk/id/eprint/77473