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Potential Scattering

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R-Matrix Theory of Atomic Collisions

Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 61))

Abstract

In this chapter we introduce the basic concepts of atomic collision theory by considering potential scattering. While being of interest in its own right, this chapter also provides a basis for our treatment of electron and positron collisions with atoms, ions and molecules in later chapters in this monograph. We commence in Sect. 1.1 by considering the solution of the non-relativistic time-independent Schrödinger equation for a short-range spherically symmetric potential. This enables us to define the scattering amplitude and various cross sections and to obtain explicit expressions for these quantities in terms of the partial wave phase shifts. We also introduce and define the K-matrix, S-matrix and T-matrix in terms of the partial wave phase shifts and we obtain an integral expression for the K-matrix and the phase shift.

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Authors and Affiliations

  1. School of Mathematics and Physics, Queen’s University, David Bates Building, Belfast, BT7 1NN, UK

    Professor Philip G. Burke

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  1. Professor Philip G. Burke
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Correspondence to Philip G. Burke .

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Burke, P.G. (2011). Potential Scattering. In: R-Matrix Theory of Atomic Collisions. Springer Series on Atomic, Optical, and Plasma Physics, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15931-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-15931-2_1

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  • Print ISBN: 978-3-642-15930-5

  • Online ISBN: 978-3-642-15931-2

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