Optical Spectroscopy of Lanthanides: Magnetic

Optical Spectroscopy of Lanthanides: Magnetic and Hyperfine Interactions represents the sixth and final book by the late Brian Wybourne, an accomplished pioneer in the spectroscopy of rare earth ions, and Lidia Smentek, a leading theoretical physicist in the field. The book provides a definitive and up-to-date theoretical description of spectroscopic properties of lanthanides doped in various materials.The book integrates computer-assisted calculations developed since Wybourne's classic publication on the topic. It contains useful Maple routines, discussions, and new aspects of the theory of f-electron systems. Establishing a unified basis for understanding state-of-the-art applications and techniques used in the field, the book reviews fundamentals based on Wybourne's graduate lectures, which include the theory of nuclei, the theory of angular momentum, Racah algebra, and effective tensor operators. It then describes magnetic and hyperfine interactions and their impact on the energy structure and transition amplitudes of the lanthanide ions. The text culminates with a relativistic description of f?f electric and magnetic dipole transitions, covering sensitized luminescence and a new parametrization scheme of f-spectra.Optical Spectroscopy of Lanthanides enables scientists to construct accurate and reliable theoretical models to elucidate lanthanides and their properties. This text is ideal for exploring a range of lanthanide applications including electronic data storage, lasers, superconductors, medicine, nuclear engineering, and nanomaterials.

Basic Facts of Nuclei	p. 1
Nucleons	p. 1
The Isotropic Harmonic Oscillator	p. 2
Magic Nuclei Numbers	p. 3
Nuclear Pairing Interactions	p. 4
Seniority and Pairing Interactions	p. 4
Nuclear Spin of Nuclei Ground States	p. 5
Nuclear Spin of H and He Isotopes	p. 6
Silicon Isotopes	p. 6
Rubidium Isotopes	p. 6
References	p. 7
Notes on the Quantum Theory of Angular Momentum	p. 9
Coupling and Uncoupling of Angular Momenta	p. 10
The 3j-Symbols	p. 12
The 6j-Symbols	p. 13
The 9j-Symbols	p. 14
Tensor Operators	p. 14
The Wigner-Eckart Theorem for SO (3)	p. 15
Coupled Tensor Operators	p. 17
Some Special 3nj Symbols	p. 18
The Zeeman Effect: Weak-Field Case	p. 19
Exercises	p. 22
References	p. 22
Interactions in One- and Two-Electron Systems	p. 25
States of Two-Electron Systems	p. 25
The Central Field Approximation	p. 26
Coulomb Interaction in Two-Electron Systems	p. 29
Coulomb Matrix Elements for the f[superscript 2] Electron Configuration	p. 32
The Spin-Orbit Interaction	p. 35
Spin-Orbit Matrices for f[superscript 2]	p. 36
Intermediate Coupling	p. 37
Exercises	p. 38
References	p. 39
Coupling Schemes of Angular Momenta	p. 41
Notes on jj coupling	p. 41
j[subscript 1]j-coupling	p. 44
Nd I and Nd II Energy Levels and j[subscript 1]j-coupling	p. 44
J[subscript 1]j-coupling in Gd III Levels of 4f[superscript 7]([superscript 8]S[subscript 7/2])6p	p. 48
J[subscript 1]l-coupling	p. 50
Exercises	p. 55
References	p. 56
Fine and Magnetic Hyperfine Structure	p. 57
Intermediate Coupling, g factors, and g-sum Rule	p. 57
Fine Structure in Alkali Atoms and Zeeman Effect	p. 59
Introductory Remarks on Magnetic Hyperfine Structure	p. 61
Magnetic Hyperfine Structure	p. 62
Exercises	p. 64
References	p. 65
Magnetic Dipole and Electric Quadrupole Hyperfine Structures	p. 67
Magnetic Hyperfine Structure in the JM[subscript j]IM[subscript l] Basis	p. 67
Zeeman Effect in the JIFM[subscript F] and JM[subscript J]IM[subscript I]M[subscript F] Bases	p. 68
Example of a J = 1/2 Electronic Level	p. 70
Example of 133/55 Cs	p. 72
Electric Quadrupole Hyperfine Structure	p. 73
Exercises	p. 76
References	p. 77
Intensities of Electronic Transitions	p. 79
Electric Dipole Transitions in Atoms	p. 80
Ratio of the Line Strengths for the D Lines of Alkali Atoms	p. 81
Line Strengths for Many-Electron Atoms	p. 82
Relative Line Strengths in LS coupling	p. 82
Relative Line Strengths for Hyperfine Levels	p. 83
Relative Line Strengths for the D2 Transitions of 87/37 Rb	p. 85
Effective Operators and Perturbation Theory	p. 85
The Quadratic Stark Effect in Atoms	p. 88
Example of 133/55 Cs	p. 90
References	p. 91
Hyperfine Interactions and Laser Cooling	p. 93
Motion and Temperature	p. 93
Some Basic Quantum Results	p. 94
Absorption and Emission of Photons	p. 95
Laser Cooling	p. 96
Magneto-Optical Traps	p. 96
References	p. 97
Ions in Crystals	p. 99
Crystal Field Splittings	p. 99
Data on the Finite Groups O
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Optical Spectroscopy of Lanthanides: Magnetic and Hyperfine Interactions

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