BASIC FACTS OF NUCLEI

Nucleons

The Isotropic Harmonic Oscillator

Magic Nuclei Numbers

Nuclear Pairing Interactions

Nuclear Spin of Nuclei Ground States

NOTES ON THE QUANTUM THEORY OF ANGULAR MOMENTUM

Coupling and Uncoupling of Angular Momenta

The 3*j*-Symbols

The 6*j*-Symbols

The 9*j*-Symbols

Tensor Operators

The Wigner-Eckart Theorem for *SO*(3)

Coupled Tensor Operators

Some Special 3*nj*-Symbols

The Zeeman Effect: Weak-Field Case

Exercises

INTERACTIONS IN ONE- AND TWO-ELECTRON SYSTEMS

States of Two-Electron Systems

The Central Field Approximation

Coulomb Interaction in Two-Electron Systems

Coulomb Matrix Elements for the *f*^{ }^{2} Electron Configuration

The Spin-Orbit Interaction

Spin-Orbit Matrices for *f*^{ }^{2}

Intermediate Coupling

Exercises

COUPLING SCHEMES OF ANGULAR MOMENTA

Notes on *jj*-coupling

*J*_{1}j*-*coupling

NdI and *NdII* Energy Levels and *j*_{1}*j*-Coupling

*J*_{1}*j*-coupling in *GdIII* Levels of 4 *f* ^{7 }(^{8}^{ }*S *_{7/}_{2 })6*p*

*J*_{1}*l*-coupling

Exercises

FINE AND MAGNETIC HYPERFINE STRUCTURE

Intermediate Coupling, *g*-Factors, and *g*-Sum Rule

Fine Structure in Alkali Atoms and Zeeman Effect

Introductory Remarks on Magnetic Hyperfine Structure

Magnetic Hyperfine Structure

Exercises

MAGNETIC DIPOLE AND ELECTRIC QUADRUPOLE HYPERFINE STRUCTURES

Magnetic Hyperfine Structure in the *JM*_{J} IM_{I} Basis

Zeeman Effect in the *JIFMF* and *JM*_{J} IM_{I} M_{F} Bases

Example of a *J* = 1/2 Electronic Level

Example of _{}

Electric Quadrupole Hyperfine Structure

Exercises

INTENSITIES OF ELECTRONIC TRANSITIONS

Electric Dipole Transitions in Atoms

Ratio of the Line Strengths for the *D* Lines of Alkali Atoms

Line Strengths for Many-Electron Atoms

Relative Line Strengths in *LS*-coupling

Relative Line Strengths for Hyperfine Levels

Relative Line Strengths for the *D*2 Transitions of _{}

Effective Operators and Perturbation Theory

The Quadratic Stark Effect in Atoms

Example of _{}

HYPERFINE INTERACTIONS AND LASER COOLING

Motion and Temperature

Some Basic Quantum Results

Absorption and Emission of Photons

Laser Cooling

Magneto-Optical Traps

IONS IN CRYSTALS

Crystal Field Splittings

Data on the Finite Groups *O* ∼ *S*_{4} and *C*_{3v} ∼ *S*_{3}

Data on the Finite Groups for Ho^{3+} Ions in LiY *F*_{4} Crystals

The Crystal Field Expansion

Point Group Symmetry Restrictions

An Octahedral Crystal Field

Identification of the Octahedral States for ^{3}^{ }*F*_{3}

Influence of the Trigonal *C*_{3v} Crystal Field

SOME ASPECTS OF CRYSTAL FIELD THEORY

Selection Rules for Transitions in Ions in a Crystal Field of *S*_{4} Point Symmetry

Crystal Field Quantum Numbers

Intensities of Transitions and Effective Operators for Ions in Crystals

A Simplified Crystal Field Calculation

The MAPLE Program

HYPERFINE INTERACTIONS IN CRYSTALS: Pr^{3+} IN OCTAHEDRAL FIELD

Matrix Elements of Magnetic Dipole Hyperfine Interactions

An Octahedral Crystal Field

Octahedral Magnetic Hyperfine Matrix Elements

MAGNETIC INTERACTIONS IN *f*-ELECTRON SYSTEMS

The *f *^{N} Electron Configurations

Calculation of the Free Ion Energy Levels of *Sm I*

The Zeeman Effect in *Sm I* (Without Nuclear Spin Effects)

The Zeeman Effect in *Sm I*, Including Nuclear Spin

Some MAPLE Zeeman Effect Programs

Zeeman Matrices in a | *JM*_{J} IM_{I} M_{F} Basis

MAGNETIC HYPERFINE INTERACTIONS IN LANTHANIDES

Magnetic Hyperfine Matrix Elements in *JMJ IMJ* Coupling

Magnetic Hyperfine Matrix Elements for the ^{7}*F J* = 0, 1 Levels

Combined Magnetic and Hyperfine Fields in *Sm I*

Combined Magnetic Hyperfine and Crystal Fields

Other Physical Mechanisms and Higher Order Corrections

Exercises

ELECTRIC QUADRUPOLE HYPERFINE INTERACTIONS

Derivation of a Tensorial Form of *H*_{EQ}

ELECTRIC QUADRUPOLE HYPERFINE STRUCTURE IN CRYSTALS

Explicit Calculation of Elliott’s Term

Spin-Orbit Interaction Between ^{7}*F*_{0} and the Lowest ^{5}*D*_{0}

THE ELECTRIC MULTIPOLE COUPLING MECHANISM IN CRYSTALS

Configuration Interaction Mechanisms

Excitations from the 4*f *^{N} Shell

Exercises

ELECTRIC DIPOLE *f*↔*f* TRANSITIONS

Judd-Ofelt Theory of *f*↔*f* Intensities

Double-Perturbation Theory

Third-Order Effective Operators

Radial Integrals and Perturbed Function Approach

Other Contributions

RELATIVISTIC EFFECTS

Relativistic Crystal Field Theory

Relativistic *f*↔*f* Transitions in Crystal Fields

Effective Operators of Relativistic *f*↔*f* Theory

Parameterization Schemes of *f* Spectra

MAGNETIC DIPOLE TRANSITIONS IN CRYSTALS

Polarization of Light and Transitions

Selection Rules for Transitions in Crystals

The Oscillator Strengths for the ^{7}*F*_{00} ↔ ^{7}*F*_{1M} Transitions

Intermediate Coupling and ^{5}*D*_{1} ↔ ^{7}*F*_{0} Transitions

Oscillator Strengths for the ^{5}*D*_{1} ↔ ^{7}*F*_{1} Magnetic Dipole Transitions

*J*-Mixing and “Intensity Borrowing”

Perturbation Approach and Higher-Order Contributions

Exercises

HYPERFINE-INDUCED TRANSITIONS

The Electron Configurations (2*s*2*p*) and (2*p*^{2}) in *N IV* Ions

Nuclear Magnetic Dipole Hyperfine Matrix Elements in (2*s*2*p*)

The Maple™ Procedures Used to Calculate the Hyperfine Matrix Elements

Hyperfine Induced *f*↔*f* Transitions

Nuclear Magnetic Hyperfine Contributions

Electric Multipole Hyperfine Contributions

Summary

Intrashell Interactions

NUMERICAL ANALYSIS OF RADIAL TERMS

Approximations

Functions of the Radial Basis Set

Perturbed Functions

Values of Radial Integrals for All Lanthanide Ions

LUMINESCENCE OF LANTHANIDE-DOPED MATERIALS

Experiments

Electrostatic Model

Effective Operator Formulation

Confrontation with Nature: Tissue Selective Lanthanide Chelates

**Index**

**Each Chapter contains Up-to-date References *