\(R\)-matrix theory of atomic collisions. Application to atomic, molecular and optical processes.
type: Item
instance of: scholarly article
title: \(R\)-matrix theory of atomic collisions. Application to atomic, molecular and optical processes.
zbMATH Open document ID: 1223.81004
DOI: 10.1007/978-3-642-15931-2
author: Philip George Burke
published in: Springer Series on Atomic, Optical, and Plasma Physics
publication date: 2010-09-30T00:00:00Z
review text: \(R\)-matrix theory was first introduced by E. P. Wigner and L. Eisenbud in the late 1940s in their analysis of nuclear resonance reactions. The fundamental idea in \(R\)-matrix theory is to partition the configuration space describing the collision process into two or more regions with the processes in each of these regions having distinctly different physical properties. A different representation of the wave function describing the process is then adopted in each region in which these wave functions are connected by the \(R\)-matrix defined on the common boundaries. Nowadays the \(R\)-matrix method, arguably, is established as the most versatile and efficient method for the modeling of scattering by electrons (and positrons) by atomic and molecular targets. This work is a fundamental monograph devoted to \(R\)-matrix theory (it is not easy to report within a short review the exact content of this book). The author describes a generalized \(R\)-matrix theory of atomic collisions and its application to the \textit{ab initio} study of atomic, molecular and optical collision processes. It is written for physicists rather than for mathematicians. The book is conceptually divided into two parts. The monograph commences by presenting an overview of the collision theory in Part I. As well as giving a self-contained summary of this theory, it also provides an introduction to the basic concepts and notation required in Part II. Chapter 1 introduces the basic concepts of atomic collision theory by considering potential scattering. The author considers the solution of the non-relativistic time-independent Schrödinger equation for a short-range spherically symmetric potential, defines the scattering amplitude and various cross sections, obtains explicit expressions for these quantities in terms of the partial wave phase shifts, and defines the \(K\)-matrix, \(S\)-matrix and \(T\)-matrix in terms of the partial wave phase shifts. The discussion is extended to the situation in …
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81V35
Mathematics Subject Classification ID: 81V45
Mathematics Subject Classification ID: 81Uxx
Mathematics Subject Classification ID: 34L25
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 35B34
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 81V80
zbMATH DE Number: 5793949
zbMATH Keywords: \(R\)-matrix theory
zbMATH Keywords: \(S\)-matrix
zbMATH Keywords: \(K\)-matrix
zbMATH Keywords: atomic molecular processes
zbMATH Keywords: optical processes
zbMATH Keywords: collisions
Wikidata QID: Q113643332
describes a project that uses: PRMAT
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-15931-2
OpenAlex ID: W4211180571
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description: scientific article; zbMATH DE number 5793949