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SOLUTION OF THE BETHE-GOLDSTONE EQUATION WITHOUT PARTIAL WAVE DECOMPOSITION

Citation

White, Larz. (2014). SOLUTION OF THE BETHE-GOLDSTONE EQUATION WITHOUT PARTIAL WAVE DECOMPOSITION. Theses and Dissertations Collection, University of Idaho Library Digital Collections. https://www.lib.uidaho.edu/digital/etd/items/white_idaho_0089e_10245.html

Title:
SOLUTION OF THE BETHE-GOLDSTONE EQUATION WITHOUT PARTIAL WAVE DECOMPOSITION
Author:
White, Larz
Date:
2014
Program:
Physics
Subject Category:
Nuclear physics
Abstract:

Nucleon-nucleon scattering is a most fundamental process in nuclear physics. From the theoretical standpoint, its description in momentum space involves the solution of an integral equation in three dimensions, which is typically accomplished with the help of a partial wave expansion of the scattering amplitude. It is the purpose of this work to present a method for solving the nucleon-nucleon scattering equation without the use of such expansion. After verifying the accuracy of our numerical tools by comparing with existing solutions of the nucleon-nucleon scattering amplitude in free space, we proceed to apply the method to the equation describing scattering of two nucleons in the nuclear medium, known as the Bethe-Goldstone equation. An important feature of this equation is the presence of the so-called "Pauli blocking operator", which prevents scattering of two fermions into occupied states, as required by the Pauli principle. In standard solution methods based on partial wave expansions, it is necessary to apply an approximation to this operator, which involves averaging over angular variables and is therefore known as the "spherical approximation". In our method, this approximation can be avoided. Thus, a focal point of this study is a comparison of Pauli blocking effects calculated in the (angle-dependent) three-dimensional formalism as compared to the usual spherical approximation. We present results for nucleon-nucleon amplitudes and observables and discuss their implications.

Description:
doctoral, Ph.D., Physics -- University of Idaho - College of Graduate Studies, 2014
Major Professor:
Sammarruca, Francesca
Committee:
Machleidt, Ruprecht; Qiang, You; Barannyk, Lyudmyla
Defense Date:
2014
Identifier:
White_idaho_0089E_10245
Type:
Text
Format Original:
PDF
Format:
application/pdf

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