I. GENERAL INTRODUCTION ....................................... 1
A. Nuclear paramagnetism ................................... 1
B. Special features of radio-frequency spectroscopy ........ 3
C. The phenomenon of resonance; 'resonant' and 'non-
resonant' methods ....................................... 4
(a) Beam measurements of atomic, molecular, and
nuclear magnetic moments ............................ 5
(b) Measurement of the magnetic moment of the neutron ... 6
(c) The fine structure of the hydrogen atom ............. 7
(d) The fine structure of positronium.................... 8
(e) The magnetic moment of the μ-meson ................. 9
(f) Resonance detected by optical means ................ 10
(g) Perturbed angular correlations ..................... 11
D. Nuclear magnetic resonance ............................. 13
(a) The principle ...................................... 13
(b) Various extensions and generalizations ............. 15
REFERENCES ................................................ 17
II. MOTION OF FREE SPINS ...................................... 19
A. Classical treatment .................................... 19
B. Quantum mechanical treatment ........................... 22
C. Quantum mechanical description of a statistical
ensemble of free spins. Density matrix ................. 24
D. Relation with the perturbation method .................. 27
E. Transient effects ...................................... 32
(a) Free precession .................................... 32
(b) Spin echoes ........................................ 33
(c) The adiabatic theorem, adiabatic passage ........... 34
F. The general problem of two levels coupled by an r.f.
field. The fictitious spin 1/2 ......................... 36
REFERENCES ................................................ 38
III. MACROSCOPIC ASPECTS OF NUCLEAR MAGNETISM .................. 39
I. Introduction ......................................... 39
A. Static susceptibility ............................. 39
B. Resonant absorption of r.f. energy ................ 40
II. The Phenomenological Equations of Bloch .............. 44
A. Steady-state solutions-saturation ................. 45
B. Steady-state solutions in an inhomogeneous
field ............................................. 49
С. Modified Bloch equations in low fields ............ 53
III. Transient Methods in Nuclear Magnetism ............... 57
A. The method of the spin echoes ..................... 58
(a) Spin diffusion ................................ 59
(b) Coherent and incoherent pulses ................ 62
B. Free precession ................................... 63
(a) Free precession in the earth's field .................. 64
C. Adiabatic passage ................................. 65
Applications of the fast-passage methods ............. 66
(а) Measurement of the relaxation time T1 ......... 66
(б) Measurement of T2 in liquids .................. 67
(c) Other applications of adiabatic fast
passage ....................................... 68
D. The method of transient nutation .................. 68
IV. Detection Methods .................................... 71
A. General ........................................... 71
B. Detection of steady-state nuclear signals ......... 75
(а) Q-meter detection ............................. 75
(б) Bridge and crossed coils methods .............. 76
(c) Marginal oscillator ........................... 77
(d) Audio-modulation, narrow ba'nd
amplification, phase sensitive detection,
signal-to-noise ratio ......................... 78
(1) Lock-in detection and signal-to-noise
ratio .................................... 79
(2) Signal-to-noise ratio .................... 82
(e) Transient effects in steady-state
detection ..................................... 85
C. Transient methods of detection .................... 86
(a) Adiabatic fast passage ........................ 86
(b) Pulse methods, coherent and incoherent
pulses ........................................ 87
D. Negative absorption—masers ........................ 89
Appendix. Proof of the Kramers-Kronig relations ........... 93
REFERENCES ................................................ 96
IV. DIPOLAR LINE WIDTH IN A RIGID LATTICE ..................... 97
I. Introduction ......................................... 97
A. The local field ................................... 97
B. General theory of magnetic absorption ............. 98
II. Broadening by Like Spins ............................ 103
A. Dipole-dipole interaction ........................ 103
B. Definition of the moments ........................ 106
C. Principle of the calculation of moments .......... 108
D. Calculation of the second and fourth moments ..... 111
E. Relationship between the line shape and the
free precession signal ........................... 114
F. A comparison between theory and experiment ....... 115
III. Dipolar Broadening by Unlike Spins .................. 122
IV. Dipolar Broadening in Magnetically Diluted
Substances .......................................... 125
A. The method of moments ............................ 125
B. The statistical theory ........................... 126
V. Modifications in the Dipolar Broadening caused
by the Existence of Quadrupole Couplings ............ 128
REFERENCES ............................................... 132
V. SPIN TEMPERATURE ......................................... 133
A. Non-interacting spins ................................. 133
B. Interacting spins in high field ....................... 136
C. Interacting spins in low fields ....................... 144
D. Zeeman system with more than one spin species ......... 150
E. Dynamics of thermal spin-spin processes ............... 154
REFERENCES ............................................... 158
VI. ELECTRON-NUCLE US INTERACTIONS ........................... 159
I. Electrostatic Couplings ............................. 159
A. The Hamiltonian .................................. 159
B. Ionic crystals ................................... 166
C. Molecular crystals ............................... 169
II. Magnetic Interactions ............................... 170
A. The coupling Hamiltonian ......................... 170
B. The effect of electron-nucleus coupling in
diamagnetic substances ........................... 173
(a) General ...................................... 173
(b) Calculation of the chemical shift ............ 175
(c) Indirect interaction between nuclear spins
in diamagnetic substances .................... 183
(1) The orbital coupling ..................... 184
(2) The Heitier-London approximation ......... 186
(3) The method of molecular orbitals ......... 190
C. The effect of electron-nucleus coupling in
paramagnetic substances .......................... 191
(а) Non-metals ................................... 191
(1) Nature of the coupling ................... 191
(2) Observability of nuclear resonance ....... 193
(б) Metals ....................................... 199
(1) The frequency shift in metals ............ 199
(2) The indirect interactions in metals ...... 206
D. Nuclear resonance in antiferromagnetic and
ferromagnetic substances ................................. 210
REFERENCES
VII. FINE STRUCTURE OF RESONANCE LINES-QUADRUPOLE EFFECTS ..... 216
I. Fine Structure caused by Dipolar Coupling ........... 216
A. Rigid lattice .................................... 216
(a) Two identical spins (two protons) I1 and
I2 ........................................... 216
(b) Systems of more than two spins ............... 222
B. Nuclear resonance in solid hydrogen .............. 223
(a) Introduction. System of two interacting
protons ...................................... 223
(b) Solid hydrogen ............................... 225
(c) Ortho- and para -hydrogen .................... 226
(d) Crystalline potential ........................ 227
(e) Magnetic resonance in a strong field ......... 228
(f) Magnetic resonance in zero field ............. 231
(g) Magnetic resonance in HD and D2 .............. 231
II. Energy Levels of Nuclear Spins in the Presence
of Quadrupole Interactions .......................... 232
A. High magnetic fields ............................. 233
(а) Energy levels in single crystals ............. 233
(б) Imperfect cubic crystals ..................... 237
(1) Powder pattern ........................... 237
(2) First-order broadening in imperfect
crystals ................................. 237
(3) Transient methods, multiple echoes ....... 241
(4) Second-order quadrupole broadening in
imperfect crystals ....................... 246
B. Low magnetic fields .............................. 249
(а) Zero field spectra ........................... 249
(1) Integer spins ............................ 250
(2) Half-integer spins ....................... 251
(б) Zeeman splittings of quadrupole levels ....... 253
(1) Integer spins ............................ 253
(2) Half-integer spins ....................... 254
(c) Transient methods ............................ 257
(1) Transient magnetization in zero field .... 257
(2) Transient magnetization in a small
magnetic field H0 ....................... 260
Appendix. Sign of the quadrupole coupling ................ 261
REFERENCES ............................................... 263
VIII.THERMAL RELAXATION IN LIQUIDS AND GASES ................. 264
I. Introduction ........................................ 264
A. Coupling of the nuclear spins with the
radiation field .................................. 264
B. Coupling of the spin system with the lattice ..... 267
II. Relaxation in Liquids and Cases .................... 268
A. General .......................................... 268
B. Definitions ...................................... 270
С. Motion of a system subject to a perturbation
which is a random function of time ............... 272
(а) Transition probability ....................... 272
(б) The master equation for populations .......... 274
(c) The master equation for the density matrix ... 276
(d) The master equation in operator form ......... 278
(e) Macroscopic differential equations ........... 280
(f) Summary of the notation introduced in this
section ...................................... 281
(g) Justification of the four assumptions
leading to the generalized master equation ... 282
D. Quantum mechanical formulation of the problem .... 283
E. Relaxation by dipolar coupling ................... 289
(а) Like spins ................................... 290
(б) Unlike spins ................................. 294
(c) Correlation functions resulting from random
molecular rotation or translation ............ 297
(1) Rotation ................................. 298
(2) Translation .............................. 300
F. Other mechanisms of relaxation in liquids ........ 305
(а) General ..................................... 305
(б) (1) Scalar spin-spin coupling ................ 306
(2) Scalar relaxation of the first kind ...... 308
(3) Scalar relaxation of the second kind ..... 309
(c) Quadrupole relaxation in liquids through
molecular reorientation ...................... 313
(d) Relaxation through anisotropic chemical
shift combined with molecular
reorientation ................................ 315
G. Nuclear relaxation in gases ...................... 316
(a) The H2 molecule-diatomic molecules ........... 316
(b) Relaxation in monatomic gases ................ 322
III. Comparison between Theory and Experiment ............ 323
A. Dipolar coupling between like spins .............. 324
(a) Short correlation times, relative values
of T1 ........................................ 324
(b) Absolute values of T1 ........................ 326
(c) Long correlation times ....................... 327
B. Coupling between unlike spins .................... 328
(a) Single irradiation methods ................... 328
(b) Double irradiation methods ................... 333
(1) The HF molecule .......................... 333
(2) Coupling between a nuclear spin and an
electronic spin .......................... 338
С. Electric quadrupole relaxation in liquids ........ 346
D. Nuclear relaxation in gases ...................... 349
(a) Nuclear relaxation in hydrogen gas ........... 349
(b) Nuclear relaxation in liquid hydrogen ........ 350
(c) Relaxation in monatomic gases ................ 352
REFERENCES ............................................... 353
IX. THERMAL RELAXATION AND DYNAMIC POLARIZATION IN SOLIDS .... 354
I. Conduction Electrons and Spin-lattice Relaxation
in Metals ........................................... 355
A. An elementary calculation of the relaxation
time ............................................. 356
B. Nuclear relaxation time and spin temperature ..... 359
C. Dynamic nuclear polarization in metals (the
Overhauser effect) ............................... 364
(a) Fermi statistics and non-equilibrium
electron spin distribution ................... 364
(b) Dynamic polarization ......................... 367
(c) Coupled equations for nuclear and electron
spin polarization ............................ 368
D. Comparison with experiment ....................... 370
(a) Measurements of T1 .......................... 370
(b) Dynamic polarization experiments ............. 373
(c) Dynamic nuclear polarization in metals at
the temperatures of liquid, helium ........... 375
II. Nuclear Relaxation caused by Fixed Paramagnetic
Impurities .......................................... 378
A. Theory ........................................... 379
B. Comparison with experiment ....................... 386
III. Magnetic Relaxation and Dynamic Polarization
in Semiconductors and Insulators .................... 389
A. Relaxation by conduction electrons in
semiconductors ................................... 389
B. Dynamic polarization by fixed paramagnetic
impurities—solid state effect .................... 392
IV. Relaxation by Thermal Vibrations in a Crystalline
Lattice ............................................. 401
A. Lattice vibrations and phonons ................... 402
B. Transition probabilities induced by the spin-
phonon coupling .................................. 404
C. Magnetic and quadrupole relaxation by spin-
phonon coupling .................................. 409
(a) Magnetic relaxation .......................... 409
(b) Quadrupole relaxation ........................ 411
D. Ultrasonic experiments ........................... 417
(a) Quadrupole transitions ....................... 419
(b) Magnetic transitions ......................... 421
REFERENCES ............................................... 423
X. THEORY OF LINE WIDTH IN THE PRESENCE OF MOTION OF THE
SPINS .................................................... 424
I. Introduction ........................................ 424
II. The Adiabatic Case .................................. 427
A. General theory ................................... 427
B. Exchange narrowing ............................... 435
C. Brownian motion narrowing ........................ 439
III. The Non-Adiabatic Line Width ........................ 441
A. Line width and transverse relaxation time ........ 441
B. General case ..................................... 442
IV. Destruction of Fine Structures through Motion ....... 447
V. Influence of Internal Motions in Solids on the
Width and Relaxation Properties of Zeeman
Resonance Lines ..................................... 451
A. Rotational motions ............................... 451
B. Translational diffusion in solids ................ 458
VI. Influence of Internal Motions in Solids on the
Width and Relaxation of Quadrupole Resonance
Lines ............................................... 467
A. Torsion oscillations ............................. 468
(a) The spin Hamiltonian ......................... 468
(b) The line width ............................... 470
(c) Relaxation time .............................. 472
(d) The spectral densities ....................... 473
B. Hindered rotations ............................... 474
(а) Fast motion .................................. 474
(б) Slow motion .................................. 477
REFERENCES ............................................... 479
XL MULTIPLET STRUCTURE OF RESONANCE LINES IN LIQUIDS ........ 480
I. Energy Levels observed by Continuous Wave Methods ... 480
A. J << δ ........................................... 482
B. J and δ comparable for two spins 1/2 ............. 484
С. J and δ comparable, for two groups G and G' of
p equivalent spins i and p' equivalent spins i',
respectively ..................................... 488
D. Perturbation method .............................. 489
E. Isochronous non-equivalent spins ................. 491
II. Multiplet Spectra observed by Transient Methods ..... 495
A. The method of free precession .................... 495
B. The method of spin echoes ........................ 497
III. Line Width Problems in Multiplet Spectra ............ 501
A. Effects of quadrupole relaxation and chemical
exchange ......................................... 501
B. Effects of magnetic relaxation ................... 506
REFERENCES ............................................... 510
XII. THE EFFECTS OF STRONG RADIO-FREQUENCY FIELDS ............. 511
I. Strong Radio-frequency Fields in Liquids ............ 511
A. 'Non-viscous liquids' ............................ 511
B. 'Viscous liquids' ................................ 517
C. Bloch equations for a 'simple' line .............. 522
D. Decoupling of spins through 'stirring' by a
radio-frequency field ............................ 527
(а) Introduction ................................. 527
(б) The intermediate pattern (elementary
theory) ...................................... 530
(c) The intermediate pattern (detailed theory).... 533
II. Strong Radio-frequency Fields in Solids ............. 539
A. Introduction ..................................... 539
B. Spin temperature in the rotating frame,
reversible fast passage .......................... 545
C. Spin temperature in the rotating frame, steady-
state solutions .................................. 555
D. Spin-lattice relaxation in the rotating frame .... 560
(a) Relaxation for a single spin species ......... 560
(b) Relaxation in the presence of two spin
species ...................................... 562
E. Double irradiation methods ....................... 566
(a) Rotary saturation ............................ 566
(1) Rotary saturation in liquids ............. 566
(2) Rotary saturation in solids .............. 569
(b) Line narrowing by double frequency
irradiation .................................. 570
(c) Transient methods of double irradiation ...... 578
REFERENCES .................................................... 580
INDEX OF NUCLEAR SPECIE'S ..................................... 583
SUBJECT INDEX ................................................. 591
|
