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Solving the Coulomb scattering problem using the complex-scaling method
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2009 (English)In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 85, no 3, 30001- p.Article in journal (Refereed) Published
Abstract [en]

We present a rigorous formalism for solving the scattering problem for long-rangeinteractions without using exact asymptotic boundary conditions. The long-range interaction maycontain both Coulomb and short-range potentials. The exterior complex-scaling method, appliedto a specially constructed inhomogeneous Schr¨odinger equation, transforms the scattering probleminto a boundary problem with zero boundary conditions. The local and integral representations forthe scattering amplitudes have been derived. The formalism is illustrated with numerical examples.

Place, publisher, year, edition, pages
Bristol, UK: IOP Publishing Ltd. , 2009. Vol. 85, no 3, 30001- p.
Keyword [en]
Scattering theory, Elastic scattering
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
URN: urn:nbn:se:su:diva-54826DOI: 10.1209/0295-5075/85/30001ISI: 000263693200001OAI: oai:DiVA.org:su-54826DiVA: diva2:398382
Funder
Swedish Research Council
Available from: 2011-02-17 Created: 2011-02-17 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Solving the quantum scattering problem for systems of two and three charged particles
Open this publication in new window or tab >>Solving the quantum scattering problem for systems of two and three charged particles
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A rigorous formalism for solving the Coulomb scattering problem is presented in this thesis. The approach is based on splitting the interaction potential into a finite-range part and a long-range tail part. In this representation the scattering problem can be reformulated to one which is suitable for applying exterior complex scaling. The scaled problem has zero boundary conditions at infinity and can be implemented numerically for finding scattering amplitudes. The systems under consideration may consist of two or three charged particles.

The technique presented in this thesis is first developed for the case of a two body single channel Coulomb scattering problem. The method is mathematically validated for the partial wave formulation of the scattering problem. Integral and local representations for the partial wave scattering amplitudes have been derived. The partial wave results are summed up to obtain the scattering amplitude for the three dimensional scattering problem. The approach is generalized to allow the two body multichannel scattering problem to be solved. The theoretical results are illustrated with numerical calculations for a number of models.

Finally, the potential splitting technique is further developed and validated for the three body Coulomb scattering problem. It is shown that only a part of the total interaction potential should be split to obtain the inhomogeneous equation required such that the method of exterior complex scaling can be applied. The final six-dimensional equation is reduced to a system of three dimensional equations using the full angular momentum representation. Such a system can be numerically implemented using the existing full angular momentum complex exterior scaling code (FAMCES). The code has been updated to solve the three body scattering problem.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2011. 64 p.
Keyword
Scattering theory, three body scattering
National Category
Atom and Molecular Physics and Optics Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:su:diva-54832 (URN)978-91-7447-213-4 (ISBN)
Public defence
2011-03-23, FA32, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Note
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Submitted. Paper 5: Manuscript.Available from: 2011-03-01 Created: 2011-02-17 Last updated: 2011-02-22Bibliographically approved

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