Angular Momentum Theory for Diatomic Molecules

Preface1 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 Problems2 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 Problems3 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 Problems4 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 Problems5 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 Problems6 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 Problems7 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? Problems8 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 Problems9 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 ProblemsAppendix 1 Algebraic Expressions for Certain n-j SymbolsAppendix 2 Four-Dimensional Spherical HarmonicsReferencesAuthor IndexSubject Index