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Potential splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulation
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
(English)Article in journal (Refereed) Submitted
Abstract [en]

In this paper we suggest a new approach for the multichannel Coulomb scattering problem. TheSchr¨odinger equation for the problem is reformulated in the form of a set of inhomogeneous equationswith a finite-range driving term. The boundary conditions at infinity for this set of equations havebeen proven to be purely outgoing waves. The formulation presented here is based on splittingthe interaction potential into a finite range core part and a long range tail part. The conventionalmatching procedure coupled with the integral Lippmann-Schwinger equations technique are usedin the formal theoretical basis of this approach. The reformulated scattering problem is suitablefor application in the exterior complex scaling technique: the practical advantage is that after thecomplex scaling the problem is reduced to a boundary problem with zero boundary conditions. TheCoulomb wave functions are used only at a single point: if this point is chosen to be at a sufficientlylarge distance, on using the asymptotic expansion of Coulomb functions, one may completely avoidthe Coulomb functions in the calculations. The theoretical results are illustrated with numericalcalculations for two models.

Keyword [en]
Scattering theory
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
URN: urn:nbn:se:su:diva-54830OAI: oai:DiVA.org:su-54830DiVA: diva2:398396
Funder
Swedish Research Council
Available from: 2011-02-17 Created: 2011-02-17 Last updated: 2011-02-18Bibliographically 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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Other links

http://arxiv.org/abs/1102.0549

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