1 Elements of Resonance ........................................ 1
1.1 Introduction ............................................ 1
1.2 Simple Resonance Theory ................................. 2
1.3 Absorption of Energy and Spin-Lattice Relaxation ........ 4
2 Basic Theory ................................................ 11
2.1 Motion of Isolated Spins-Classical Treatment ........... 11
2.2 Quantum Mechanical Description of Spin in a Static
Field .................................................. 13
2.3 Equations of Motion of the Expectation Value ........... 17
2.4 Effect of Alternating Magnetic Fields .................. 20
2.5 Exponential Operators .................................. 25
2.6 Quantum Mechanical Treatment of a Rotating Magnetic
Field .................................................. 29
2.7 Bloch Equations ........................................ 33
2.8 Solution of the Bloch Equations for Low H1 ............. 35
2.9 Spin Echoes ............................................ 39
2.10 Quantum Mechanical Treatment of the Spin Echo .......... 46
2.11 Relationship Between Transient and Steady-State
Response of a System and of the Real and Imaginary
Parts of the Susceptibility ............................ 51
2.12 Atomic Theory of Absorption and Dispersion ............. 59
3 Magnetic Dipolar Broadening of Rigid Lattices ............... 65
3.1 Introduction ........................................... 65
3.2 Basic Interaction ...................................... 66
3.3 Method of Moments ...................................... 71
3.4 Example of the Use of Second Moments ................... 80
4 Magnetic Interactions of Nuclei with Electrons .............. 87
4.1 Introduction ........................................... 87
4.2 Experimental Facts About Chemical Shifts ............... 88
4.3 Quenching of Orbital Motion ............................ 89
4.4 Formal Theory of Chemical Shifts ....................... 92
4.5 Computation of Current Density ......................... 96
4.6 Electron Spin Interaction ............................. 108
4.7 Knight Shift .......................................... 113
4.8 Single Crystal Spectra ................................ 127
4.9 Second-Older Spin Effects-Indirect Nuclear Coupling ... 131
5 Spin-Lattice Relaxation and Motional Narrowing of
Resonance Lines ............................................ 145
5.1 Introduction .......................................... 145
5.2 Relaxation of a System Described by a Spin
Temperature ........................................... 146
5.3 Relaxation of Nuclei in a Metal ....................... 151
5.4 Density Matrix-General Equations ...................... 157
5.5 The Rotating Coordinate Transformation ................ 165
5.6 Spin Echoes Using the Density Matrix .................. 169
5.7 The Response to a δ-Function .......................... 174
5.8 The Response to а π/2 Pulse: Fourier Transform NMR .... 179
5.9 The Density Matrix of a Two-Level System .............. 186
5.10 Density Matrix-An Introductory Example ................ 190
5.11 Bloch-Wangsness-Redfield Theory ....................... 199
5.12 Example of Redfield Theory ............................ 206
5.13 Effect of Applied Alternating Fields .................. 215
6 Spin Temperature in Magnetism and in Magnetic Resonance .... 219
6.1 Introduction .......................................... 219
6.2 A Prediction from the Bloch Equations ................. 220
6.3 The Concept of Spin Temperature in the Laboratory
Frame in the Absence of Alternating Magnetic Fields ... 221
6.4 Adiabatic and Sudden Changes .......................... 223
6.5 Magnetic Resonance and Saturation ..................... 231
6.6 Redfield Theory Neglecting Lattice Coupling ........... 234
6.6.1 Adiabatic Demagnetization in the Rotating
Frame .......................................... 235
6.6.2 Sudden Pulsing ................................. 237
6.7 The Approach to Equilibrium for Weak H1 ............... 239
6.8 Conditions for Validity of the Redfield Hypothesis .... 241
6.9 Spin-Lattice Effects .................................. 242
6.10 Spin Locking, T1q', and Slow Motion .................... 244
7 Double Resonance ........................................... 247
7.1 What Is Double Resonance and Why Do It? ............... 247
7.2 Basic Elements of the Overhauser-Pound Family of
Double Resonance ...................................... 248
7.3 Energy Levels and Transitions of a Model System ....... 250
7.4 The Overhauser Effect ................................. 254
7.5 The Overhauser Effect in Liquids: The Nuclear
Overhauser Effect ..................................... 257
7.6 Polarization by Forbidden Transitions: The Solid
Effect ................................................ 264
7.7 Electron-Nuclear Double Resonance (ENDOR) ............. 266
7.8 Bloembergen's Three-Level Maser ....................... 269
7.9 The Problem of Sensitivity ............................ 270
7.10 Cross-Relaxation Double Resonance ..................... 271
7.11 The Bloembergen-Sorokin Experiment .................... 275
7.12 Hahn's Ingenious Concept .............................. 277
7.13 The Quantum Description ............................... 279
7.14 The Mixing Cycle and Its Equations .................... 283
7.15 Energy and Entropy .................................... 287
7.16 The Effects of Spin-Lattice Relaxation ................ 289
7.17 The Pines-Gibby-Waugh Method of Cross Polarization .... 293
7.18 Spin-Coherence Double Resonance-Introduction .......... 295
7.19 A Model System-An Elementary Experiment: The S-Flip-
Only Echo ............................................. 296
7.20 Spin Decoupling ....................................... 303
7.21 Spin Echo Double Resonance ............................ 311
7.22 Two-Dimensional FT Spectra-The Basic Concept .......... 319
7.23 Two-Dimensional FT Spectra-Line Shapes ................ 324
7.24 Formal Theoretical Apparatus I-The Time Development
of the Density Matrix ................................. 325
7.25 Coherence Transfer .................................... 331
7.26 Formal Theoretical Apparatus II-The Product Operator
Method ................................................ 344
7.27 The Jeener Shift Correlation (COSY) Experiment ........ 350
7.28 Magnetic Resonance Imaging ............................ 357
8 Advanced Concepts in Pulsed Magnetic Resonance ............. 367
8.1 Introduction .......................................... 367
8.2 The Сагг-Purcell Sequence ............................. 367
8.3 The Phase Alternation and Meiboom-Gill Methods ........ 369
8.4 Refocusing Dipolar Coupling ........................... 371
8.5 Solid Echoes .......................................... 371
8.6 The Jeener-Broekaert Sequence for Creating Dipolar
Order ................................................. 380
8.7 The Magic Angle in the Rotating Frame- The Lee-
Goldburg Experiment ................................... 384
8.8 Magic Echoes .......................................... 388
8.9 Magic Angle Spinning .................................. 392
8.10 The Relation of Spin-Flip Narrowing to Motional
Narrowing ............................................. 406
8.11 The Formal Description of Spin-Flip Narrowing ......... 409
8.12 Observation of the Spin-Flip Narrowing ................ 416
8.13 Real Pulses and Sequences ............................. 421
8.13.1 Avoiding a z-Axis Rotation ..................... 421
8.13.2 Nonideality of Pulses .......................... 422
8.14 Analysis of and More Uses for Pulse Sequence .......... 423
9 Multiple Quantum Coherence ................................. 431
9.1 Introduction .......................................... 431
9.2 The Feasibility of Generating Multiple Quantum
Coherence-Frequency Selective Pumping ................. 434
9.3 Nonselective Excitation ............................... 444
9.3.1 The Need for Nonselective Excitation ........... 444
9.3.2 Generating Multiple Quantum Coherence .......... 445
9.3.3 Evolution, Mixing, and Detection of Multiple
Quantum Coherence .............................. 449
9.3.4 Three or More Spins ............................ 455
9.3.5 Selecting the Signal of a Particular Order of
Coherence ...................................... 463
9.4 High Orders of Coherence .............................. 470
9.4.1 Generating a Desired Order of Coherence ........ 471
9.4.2 Mixing to Detect High Orders of Coherence ...... 480
10 Electric Quadrupole Effects ................................ 485
10.1 Introduction .......................................... 485
10.2 Quadrupole Hamiltonian-Part 1 ......................... 486
10.3 Clebsch-Gordan Coefficients, Irreducible Tensor
Operators, and the Wigner-Eckart Theorem .............. 489
10.4 Quadrupole Hamiltonian-Part 2 ......................... 494
10.5 Examples at Strong and Weak Magnetic Fields ........... 497
10.6 Computation of Field Gradients ........................ 500
11 Electron Spin Resonance .................................... 503
11.1 Introduction .......................................... 503
11.2 Example of Spin-Orbit Coupling and Crystalline
Fields ................................................ 505
11.3 Hyperfine Structure ................................... 516
11.4 Electron Spin Echoes .................................. 524
11.5 Vk Center ............................................. 533
12 Summary .................................................... 555
Problems ...................................................... 557
Appendixes .................................................... 579
A. A Theorem About Exponential Operators .................. 579
B. Some Further Expressions for the Susceptibility ........ 580
C. Derivation of the Correlation Function for a Field
That Jumps Randomly Between ±h0 ........................ 584
D. A Theorem from Perturbation Theory ..................... 585
E. The High Temperature Approximation ..................... 589
F. The Effects of Changing the Precession Frequency-
Using NMR to Study Rate Phenomena ...................... 592
G. Diffusion in an Inhomogeneous Magnetic Field ........... 597
H. The Equivalence of Three Quantum Mechanics Problems .... 601
I. Powder Patterns ........................................ 605
J. Time-Dependent Hamiltonians ............................ 616
K. Conection Terms in Average Hamiltonian Theory - The
Magnus Expansion ....................................... 623
Selected Bibliography ......................................... 629
References .................................................... 639
Author Index .................................................. 647
Subject Index ................................................. 651
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