The study which fonns the second volume of this series deals with the interplay of groups and composite particle theory in nuclei. Three main branches of ideas are de veloped and linked with composite particle theory: the pennutational structure of the nuclear fermion system, the classification scheme based on the orbital partition and the associated supennuitiplets, and the representation in state space of geometric trans fonnations in classical phase space. One of the authors (p. K.) had the opportunity to present some of the ideas under lying this work at the 15th Solvay Conference on Symmetry Properties of Nuclei in 1970. Since this time, the authors continued their joint effort to decipher the conceptual struc ture of composite particle theory in tenns of groups and their representations. The pattern of connections is fully developed in the present study. The applications are carried to the points where the impact of group theory may be recognized. The range of applications in our opinion goes far beyond these points.
1 Introduction.- 2 Permutational Structure of Nuclear States.- 2.1
Concepts and Motivation.- 2.2 The Symmetric Group S(n).- 2.3 Irreducible
Representations of the Symmetric Group S(n).- 2.4 Construction of States of
Orbital Symmetry, Young Operators.- 2.5 Computation of Irreducible
Representations of the Symmetric Group.- 2.6 Spin, Isospin and the
Supermultiplet Scheme.- 2.7 Matrix Elements in the Supermultiplet Scheme.-
2.8 Supermultiplet Expansion for States of Light Nuclei.- 2.9 Notes and
References.- 3 Unitary Structure of Orbital States.- 3.1 Concepts and
Motivation.- 3.2 The General Linear and the Unitary Group and Their
Finite-Dimensional Representations.- 3.3 Wigner Coefficients of the Group
GL(j, C).- 3.4 Computation of Irreducible Representations of GL(j, C) from
Double Gelfand Polynomials.- 3.5 Computation of Irreducible Representations
of GL(j,C) from Representations of the Symmetric Group S (n).- 3.6
Conjugation Relations of Irreducible Representations of GL (j, C).- 3.7
Fractional Parentage Coefficients and Their Computation.- 3.8 Bordered
Decomposition of Irreducible Representations for the Group GL(j, C).- 3.9
Orbital Configurations of n Particles.- 3.10 Decomposition of Orbital Matrix
Elements.- 3.11 Orbital Matrix Elements for the Configuration f = [ 4j].- 3.12
Notes and References.- 4 Geometric Transformations in Classical Phase Space
and their Representation in Quantum Mechanics.- 4.1 Concepts and Motivation.-
4.2 Symplectic Geometry of Classical Phase Space.- 4.3 Basic Structure of
Bargmann Space.- 4.4 Representation of Translations in Phase Space by Weyl
Operators.- 4.5 Representation of Linear Canonical Transformations.- 4.6
Oscillator States of a Single Particle with Angular Momentum and Matrix
Elements of Some Operators.- 4.7 Notes and References.- 5 Linear Canonical
Transformations and Interacting n-particle Systems.- 5.1 Orthogonal Point
Transformations in n-particle Systems and their Representations.- 5.2 General
Linear Canonical Transformations for n Particles and State Dilatation.- 5.3
Interactions in n-body Systems and Complex Extension of Linear Canonical
Transformations.- 5.4 Density Operators.- 5.5 Notes and References.- 6
Composite Nucleon Systems and their Interaction.- 6.1 Concepts and
Motivation.- 6.2 Configurations of Composite Nucleon Systems.- 6.3 Projection
Equations and Interaction of Composite Nucleon Systems.- 6.4 Phase Space
Transformations for Configurations of Oscillator Shells and for Composite
Nucleon Systems.- 6.5 Interpretation of Composite Particle Interaction in
Terms of Single-Particle Configurations.- 6.6 Notes and References.- 7
Configurations of Simple Composite Nucleon Systems.- 7.1 Concepts and
Motivation.- 7.2 Normalization Kernels.- 7.3 Interaction Kernels.- 7.4
Configurations of Three Simple Composite Nucleon Systems.- 7.5 Notes and
References.- 8 Interaction of Composite Nucleon Systems with Internal Shell
Structure.- 8.1 Concepts and Motivation.- 8.2 Single-Particle Bases and their
Overlap Matrix.- 8.3 The Normalization Operator for Two-Center Configurations
with a Closed Shell and a Simple Composite Particle Configuration.- 8.4 The
Interaction Kernel for Two-Center Configurations with a Closed Shell and a
Simple Composite Particle Configuration.- 8.5 Two Composite Particles with
Closed-Shell Configurations.- 8.6 Two-Center Configurations with an Open
Shell and a Simple Composite Particle Configuration.- 8.7 Notes and
References.- 9 Internal Radius and Dilatation.- 9.1 Oscillator States of
Different Frequencies.- 9.2 Dilatations in Different Coordinate Systems.- 9.3
Dilatations of Simple Composite Nucleón Systems.- 9.4 Notes and References.-
10 Configurations of Three Simple Composite Particles and the Structure of
Nuclei with Mass Numbers A = 410.- 10.1 Concepts and Motivation.- 10.2 The
Model Space.- 10.3 The Interaction.- 10.4 Convergence Properties of the Model
Space.- 10.5 Comparison with Shell Model Results.- 10.6 Absolute Energies.-
10.7 The Oscillator Parameter b.- 10.8 Results on Nuclei with A = 410.- 10.9
Notes and References.- References for Sections 19.- References for Section
10.
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