# Angular Momentum Theory for Diatomic Molecules

## 1st Edition

**Authors:**Brain Judd

**eBook ISBN:**9780323159050

**Imprint:**Academic Press

**Published Date:**1st January 1975

**Page Count:**250

## Description

Angular Momentum Theory for Diatomic Molecules focuses on the application of angular momentum theory in describing the complex dynamical processes in molecules.

The manuscript first offers information on tensor algebra and rotation group. Discussions focus on commutation relations, spherical and double tensors, rotations, coupling, reduced matrix elements, quaternions, combination theorem for Gegenbauer polynomials, and combination theorems for spherical harmonics. The book then takes a look at R(4) in physical systems and hydrogen molecular ion, including rigid rotator, reversed angular momentum, reduced matrix elements, spheroidal coordinates, and hydrogen atom in spheroidal coordinates.

The publication examines expansions and free diatomic molecules. Topics include angular momentum, molecular frame, primitive energy spectrum, rotating oscillator and hydrogen atom, expressions for electric potentials, delta functions, and Neumann expansion. The manuscript also considers external fields and perturbations.

The text is a dependable reference for readers interested in the application of angular momentum theory in identifying the dynamical processes going on in molecules.

## Table of Contents

Preface

1 Tensor Algebra

1.1 Introduction

1.2 Commutation Relations

1.3 Rotations

1.4 Rotation Matrices

1.5 Spherical Tensors

1.6 Double Tensors

1.7 Coupling

1.8 Integrals over the Rotation Matrices

1.9 The Wigner-Eckart Theorem

1.10 Reduced Matrix Elements

1.11 The 9-j Symbol

1.12 The 6-j Symbol

Problems

2 The Rotation Group R(4)

2.1 Groups

2.2 Generators for R(4)

2.3 Quaternions

2.4 Four-Dimensional Spherical Harmonics

2.5 Phases

2.6 CG Coefficients for R(4)

2.7 Combination Theorem for Gegenbauer Polynomials

2.8 Combination Theorems for Spherical Harmonics

2.9 Addition Theorems

2.10 Expansions on and off the Hypersphere

Problems

3 R(4) in Physical Systems

3.1 The Rigid Rotator

3.2 Reversed Angular Momentum

3.3 Reduced Matrix Elements

3.4 Momentum Space

3.5 The Coulomb Potential

3.6 Four-Dimensional Momentum Space

3.7 The Hydrogen Atom

3.8 The Lenz Vector

Problems

4 The Hydrogen Molecular Ion

4.1 Introduction

4.2 Spheroidal Coordinates

4.3 The Generalized Hydrogen Molecular Ion

4.4 The Hydrogen Atom in Spheroidal Coordinates

4.5 The Spectrum of the Separation Constant f

4.6 A Two-Center System with ZA ۠ZB

4.7 Elementary Solutions to the Generalized Hydrogen Molecular Ion

4.8 The Many-Center Problem

4.9 Evaluation of STt(R)

4.10 Limited Bases

4.11 Higher Groups

4.12 The Group 0(2, 1) and the (m, n) Symmetry

Problems

5 Expansions

5.1 General Method

5.2 Expressions for Electric Potentials

5.3 Delta Functions

5.4 Bipolar Expansions

5.5 The Neumann Expansion

5.6 Ruedenberg's Method

5.7 Electric Quadrupole-Quadrupole Interaction

Problems

6 Free Diatomic Molecules

6.1 Angular Momentum

6.2 The Molecular Frame

6.3 An Added Variable

6.4 Generators of R(4)

6.5 The Total Spin-Independent Hamiltonian

6.6 The Primitive Energy Spectrum

6.7 The Rotating Oscillator and the Hydrogen Atom

6.8 Spin

6.9 Electronic Structure

6.10 Intrinsic Parity

6.11 Parity

Problems

7 The Hydrogen Molecule

7.1 Introduction

7.2 The Effective Fine-Structure Hamiltonian

7.3 Fine Structure

7.4 Spin-Spin Interaction

7.5 The United-Atom Approximation

7.6 The Spin-Rotation Interaction

7.7 Effective Operators

7.8 Hyperfine Interaction

7.9 The Ground State 1?

Problems

8 External Fields

8.1 Introduction

8.2 The Stark Effect

8.3 The Zeeman Effect

8.4 Diagonal Corrections to Hz

8.5 Transitions between Molecular States

8.6 Electric-Dipole Transitions

8.7 Line Strengths

8.8 Magnetic-Dipole and Quadrupole Radiation

8.9 Classical Limits

Problems

9 Perturbations

9.1 Intermediate Coupling

9.2 A-Doubling

9.3 Corrections to gr

9.4 Diamagnetic Shielding

9.5 Homomorphic Perturbations

9.6 Centrifugal Corrections

9.7 Spectroscopic Perturbations

9.8 Forbidden Transitions

Problems

Appendix 1 Algebraic Expressions for Certain n-j Symbols

Appendix 2 Four-Dimensional Spherical Harmonics

References

Author Index

Subject Index

## Details

- No. of pages:
- 250

- Language:
- English

- Copyright:
- © Academic Press 1975

- Published:
- 1st January 1975

- Imprint:
- Academic Press

- eBook ISBN:
- 9780323159050