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Title:  A variational theory of nuclear matter 
Author(s):  Wiringa, Robert Bruce 
Doctoral Committee Chair(s):  Pandharipande, V.R. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  variational theory
nuclear matter astrophysics nucleonnucleon potentials 
Abstract:  The hypotheticai system of nucleons known as nuclear matter provides a very interesting field of study with relevance to both nuclear physics and astrophysics. The task of finding nucleonnucleon potentials that explain the empirical properties of nuclear matter, as well as the twobody data, has been hampered by the lack of an adequate manybody theory for treating the complicated forces involved. Realistic nucleonnucleon potentials have strong spin, isospin, tensor and spinorbit components which induce correspondingly strong correlations in nuclear matter. In this thesis we present a variational theory designed to cope with these complicated correlations. To place the theory in perspective we give an overview of several different manybody theories and compare their predictions in the somewhat simpler systems of the 4He and 3He liquids, and for a simple central potential model of nuclear matter. The variational theory is then developed, starting with the choice of wave function. A generalized Jastrow product of twobody correlation functions containing central, spin, isospin, tensor, and spinorbit operators is used. The correlation function is generated by a series of twobody Schrodinger equations with boundary conditions which require the wave function to heal at a distance d. The wave function is parameterized by d and by the magnitudes of the noncentral correlations. Expectation values with variational wave functions of the Jastrow type may be studied conveniently with generalized Mayer diagrams. Diagram rules are given and a general diagrammatic cluster expansion is derived. It is an expansion in powers of commutators of the noncentral operators, and in their absence reduces to the usual Mayer cluster expansion. Evaluation of diagrams in the cluster expansion is complicated by the presence of the noncommuting operators. Some simple rules and useful methods for calculating the contribution due to the central, spin, isospin, and tensor operators are given. Spinorbit operators are neglected beyond this point, but the approach used is extendible to them. Large classes of diagrams contributing to an expectation value can be summed by means of integral equations. The development of single chain, hypernetted chain, and Fermi hypernetted chain (FHNC) equations for central correlations is reviewed. The chain summation methods are extended to sum single operator chains (SOC) for the noncentral operators. Methods are also given for treating the leading commutator corrections in the expansi0n by simple vertex factors. The energy expectation value for potentials with six operators are evaluated using the FHNC/SOC functions, with an exact treatment of the commutators involved. The energy is found to have a minimum with respect to variations in all parameters. Results of calculations with model potentials based on the Reid, BetheJohnson, HamadaJohnston, and GammelThaler potentials are reported. A crude estimate of the effect of the neglected spinorbit potentials on the nuclear matter binding energy and saturation density indicates that it could be significant. A correct treatment of the spinorbit potentials is the next major step that should be taken. 
Issue Date:  1978 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/25583 
Rights Information:  1978 Robert Bruce Wiringa 
Date Available in IDEALS:  20110629 
Identifier in Online Catalog:  356092 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics