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R-MATRIX APPROACH WITH PROPER BOUNDARY CONDITIONS FOR
COLLISION PROCESSES
by
Hao Xu
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)
May 2011
Copyright 2011 Hao Xu
Object Description
| Title | R-matrix approach with proper boundary conditions for collision processes |
| Author | Xu, Hao |
| Author email | xuh@usc.edu; ragioneman@hotmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Physics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2011-01-25 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-03-29 |
| Advisor (committee chair) | Shakeshaft, Robin |
| Advisor (committee member) |
Chang, Tu-Nan Däppen, Werner Haas, Stephan Kunc, Joseph A. |
| Abstract | We develop an R-matrix approach for treating collision processes which explicitly takes into account, by means of a simple energy-dependent analytic function, the out-of-phase oscillations of the incident and scattered standing waves in the interior region. Thereby we avoid the use of the Bloch operator. In place of the Bloch operator the incident wave provides the source term in an inhomogeneous equation for the scattered wave. A hybrid basis composed of both Ricatti-Bessel and Sturmian functions is used to expand the scattered wave. We take those channels not treated exactly into account via the optical potential, which is generally nonHermitian due to dissipation at the boundary. The optical potential is constructed on a real analytic basis using a resolvent that satisfies outgoing-wave boundary conditions. The K-matrix is directly determined by matching the interior wavefunction and its derivative at the boundary to the exterior ones. We have tested our method by applying it to one-photon single-ionization of He(1s²) accompanied by excitation to He⁺(2s/2p). In the near threshold region, we find a cusp in the partial cross sections at the threshold. At higher energies, excellent agreement with experiment is obtained for the cross sections, both for photoionization to He⁺(n=1) and to He⁺(n=2). We have also applied our method to the electron impact He⁺ excitation problem. The partial cross sections for 1s-2s and 1s-2p excitations with total orbital angular momenta L≤2 have been calculated and compared to other theoretical results. |
| Keyword | R-matrix; collision processes; Helium photoionization; electron-impact excitation of Helium ion |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3710 |
| Contributing entity | University of Southern California |
| Rights | Xu, Hao |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@dots.usc.edu |
| Filename | etd-Xu-4416 |
| Archival file | uscthesesreloadpub_Volume51/etd-Xu-4416.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | R-MATRIX APPROACH WITH PROPER BOUNDARY CONDITIONS FOR COLLISION PROCESSES by Hao Xu A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) May 2011 Copyright 2011 Hao Xu |
