Dissertation
Reaction mechanisms in many-body scattering theory
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Spring 2025
DOI: 10.25820/etd.007822
Abstract
The exact solution of the many-body scattering problem is an intractable numerical problem due to the large dimension of the many-body Hilbert space, and this can be seen by the large number of energetically open channels in a nuclear reaction. Even if the problem could be solved numerically, the solution does not determine the role of different scattering channels and how they interact in a given reaction.
In certain reactions, most of the scattered flux will remain in a small subset of important channels. When this is the case, one can use partition combinatorics associated with the partition lattice to decompose a many-body Hamiltonian into a linear combination of proper subsystem Hamiltonians, and the spectral decomposition of these proper subsystem Hamiltonians can be expressed as a sum of channel contributions. By retaining a subset of channels, one obtains a truncated Hamiltonian that satisfies an optical theorem in the set of retained channels. When the retained channels only include two- and three-body channels, the many-body system becomes a set of coupled few-body systems. If only two-body channels are included, then one obtains truncated equations for 2-cluster scattering that are essentially just a set of coupled Lippmann-Schwinger equations that can be solved using numerical two-body methods.
In this work, I will discuss a numerical method for two-body scattering that can be generalized to 2-cluster scattering with multiple channels. I will also demonstrate the utility of using partition combinatorics in nuclear reaction theory by applying partition combinatorics to a calculation involving deuteron-alpha scattering.
Details
- Title: Subtitle
- Reaction mechanisms in many-body scattering theory
- Creators
- Brady J Martin
- Contributors
- Wayne N. Polyzou (Advisor)Vincent G J Rodgers (Committee Member)Mary Hall Reno (Committee Member)Palle E. T. Jorgensen (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Physics
- Date degree season
- Spring 2025
- DOI
- 10.25820/etd.007822
- Publisher
- University of Iowa
- Number of pages
- xiv, 141pages
- Copyright
- Copyright 2025 Brady J Martin
- Language
- English
- Date submitted
- 04/28/2025
- Description illustrations
- illustrations, graphs, tables
- Description bibliographic
- Includes bibliographical references (pages 112-113).
- Public Abstract (ETD)
- The two-body scattering problem can be solved analytically for some interactions, and it is relatively simple to solve using numerical methods when dealing with complex interactions. Although two-body scattering calculations are relatively straightforward, scattering calculations for systems of three or more particles are much more complicated. In two-particle collisions, there are two incoming particles before the collision and two outgoing particles after the collision. In collisions involving three or more particles, there are multiple possible outgoing configurations of particles given a particular initial configuration of particles. The many-body scattering problem is an extremely difficult problem to solve, but there are mathematical and computational methods that can be used to simplify the calculations. One of the mathematical frameworks for tackling the many-body scattering problem is called the partition lattice, and it allows one to approximate a many-body system as a set of coupled two-body systems. This means that one can use two-body scattering methods when performing calculations. In this work, I will discuss a numerical method for two-body scattering that can be generalized for many-body scattering. I will also demonstrate the utility of using the partition lattice in many-body scattering calculations by applying the framework to a calculation involving deuteron-alpha scattering.
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984830726902771
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