Overview

These lectures deal with quantum mechanical two-, three-, and four-body systems. The dynamical equations are presented together with approximate methods of solution. Examples dealing with realistic few-body nuclear systems illustrate the working of these approaches, quite a few of which are not discussed in standard textbooks on quantum mechanics. In contrast to the usual treatment, we deal not only with nucleonic but also with non-nucleonic degrees of freedom. These lectures introduce uninitiated readers to the particulars of few-body systems, and lead them through various useful approaches and approximations. They provide the tools and expertise necessary for independent calculations and research in this field. Besides covering the traditional topics, different versions of finite-dimensional approximations of the potential, an exhaustive review of methods of solving three-body equations, and the differential form of the approximate four-body and Yakubovsky equations are given.

Full Product Details

Author:   Vladimir B. Belyaev ,  G. B. Pontecorvo
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.375kg
ISBN:  

9783540185871

ISBN 10:   3540185879
Pages:   144
Publication Date:   20 July 1990
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. The Two-Body Problem.- 1.1 Properties of the Two-Particle t-Matrix.- 1.2 Phase-Equivalent Potentials.- 1.3 Separable Expansions of the t-Matrix.- 2. The Fadeev-Equations in the Three-Body Problem. Pion-Nucleus Scattering.- 2.1 General Remarks.- 2.2 Formal Derivations for Transition Amplitudes and Wave Functions.- 2.3 Scattering of a Particle on a Bound Pair.- 2.4 Interpolation Method in the Solution of the Faddeev Equations.- 2.5 The Alt-Grassberger-Sandhas Form of the Faddeev Equations.- 2.6 The Karlsson and Zeiger Form of the Faddeev Equations.- 2.7 Solution by Means of the Method of Moments and Spline Functions.- 2.8 Unitarization of Approximate Solutions.- 2.9 Dispersion Methods in the Three-Body Problem.- 2.10 Unitarization Based on the Evolutionary Coupling Constant (ECC) Method.- 2.11 Splitting of the Three-Particle Wave Function into Internal and External Parts.- 3. The Four-Body Problem.- 3.1 The Integral and Differential Yakubovsky Equation.- 3.2 Four-Particle AGS Equations.- 3.3 Approximate Four-Particle Equations for the ? (3N) System.- 3.4 Scattering of n(p) by Nuclei Consisting of Three Nucleons at Low Energies.- 3.5 NN-Scattering in the Nonrelativistic Quark Model (The Six-Body Problem).- 4. Related Problems.- 4.1 The Faddeev Equations and the Heisenberg Ferromagnetic.- 4.2 Sum Rules andvirial Coefficients.- 4.3 Systems Involving Variable Numbers of Particles.- 5. Outlook.- General Reading.- References.

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