Atomic and Laser Spectroscopy

CONTENTS......Page 10
1.1. Planck\'s radiation law......Page 20
1.2. The photoelectric effect......Page 23
1.3. Early atomic spectroscopy......Page 24
1.4. The postulates of Bohr\'s theory of atomic structure......Page 26
1.5. Development of quantum mechanics......Page 28
1.7. Optical physics since 1945......Page 30
1.8. The present situation (1975)......Page 31
Problems......Page 32
References......Page 34
General references and further reading......Page 35
2.1. Maxwell\'s equations......Page 36
2.2. The electromagnetic wave equations......Page 39
2.3. Plane wave solutions......Page 41
2.4. Linear and circular polarizations......Page 43
2.5. The energy density and the Poynting vector......Page 47
2.6. Vector and scalar potentials......Page 49
2.7. Electric dipole radiation......Page 52
2.8. Rate of radiation by an electric dipole oscillator......Page 58
2.9. Angular momentum of dipole radiation......Page 59
2.10. Magnetic dipole radiation......Page 62
2.11. Electric quadrupole radiation......Page 63
2.12. Multipole fields......Page 67
Problems......Page 68
General references and further reading......Page 70
3.1. The Schrödinger wave equation......Page 71
3.2. Expectation values and matrix elements......Page 74
3.3. Solution of Schrödinger\'s equation for spherically symmetric potentials......Page 75
3.4. Orbital angular momentum......Page 80
3.5. Hydrogenic wave functions......Page 81
3.6. Spin angular momentum......Page 86
3.7. Coupling of two angular momenta......Page 88
3.8. Spin-orbit interaction and the vector model......Page 92
3.9. Many-electron atoms......Page 96
Problems......Page 107
General references and further reading......Page 110
4.1. The classical atomic model......Page 112
4.2. Radiative lifetime of a classical atom......Page 114
4.3. Spontaneous emission probability, A[sub(ki)]......Page 116
4.4. Spontaneous emission according to quantum electrodynamics......Page 119
4.5. Spontaneous transitions between degenerate levels......Page 121
4.6. Radiative lifetimes of excited atoms......Page 122
4.7. Intensity of light emitted by optically thin sources......Page 123
4.8. Oscillator strengths......Page 125
4.10. Oscillator strengths in hydrogenic systems......Page 128
4.11. Theoretical oscillator strengths in complex atoms......Page 133
Problems......Page 134
General references and further reading......Page 137
5.2. One-electron atoms without spin......Page 139
5.3. One-electron atoms with spin......Page 147
5.4. Tensor properties of the electric dipole operator......Page 148
5.5. Many-electron atoms......Page 150
5.6. Relative intensities in L-S coupling and forbidden transitions......Page 157
Problems......Page 158
General references and further reading......Page 160
6. MEASUREMENT OF RADIATIVE LIFETIMES OF ATOMS AND MOLECULES......Page 161
6.1. The beam-foil method......Page 162
6.2. Fast beam experiments using laser excitation......Page 178
6.3. The delayed-coincidence method using electron excitation......Page 179
6.4. Delayed-coincidence experiments using optical excitation......Page 190
References......Page 195
General references and further reading......Page 196
7. FORBIDDEN TRANSITIONS AND METASTABLE ATOMS......Page 197
7.1. Magnetic dipole transitions......Page 199
7.2. Electric quadrupole radiation......Page 202
7.3. Selection rules for magnetic dipole and electric quadrupole transitions......Page 204
7.4. Two-photon decay of hydrogenic systems......Page 208
7.5. Forbidden transitions in helium-like systems......Page 222
7.6. Collision processes involving metastable atoms......Page 233
Problems......Page 243
References......Page 245
General references and further reading......Page 247
8. THE WIDTH AND SHAPE OF SPECTRAL LINES......Page 248
8.1. The natural or radiative lineshape......Page 249
8.2. The pressure broadening of spectral lines......Page 255
8.3. Doppler broadening......Page 267
8.4. Comparison of Doppler, collision, and natural widths......Page 270
8.5. Voigt profiles......Page 271
8.6. Effect of the instrumental profile......Page 272
8.7. Line profile measurements at low pressures and temperatures......Page 276
Problems......Page 285
References......Page 288
General references and further reading......Page 289
9.1. Classical description of absorption by electric dipole oscillator......Page 290
9.2. Einstein\'s treatment of stimulated emission and absorption......Page 293
9.3. The semi-classical treatment of absorption and induced emission......Page 297
9.4. Einstein B-coefficients defined in terms of intensity......Page 302
9.5. Relations between Einstein B-coefficients and f-values......Page 303
9.7. Introduction of the atomic frequency response......Page 304
Problems......Page 305
General references and further reading......Page 307
10.1. Derivation of the equation of transfer......Page 308
10.2. Solution of the transfer equation for uniformly excited sources......Page 311
10.4. Equivalent widths of absorption lines......Page 315
10.5. Measurement of relative f-values by absorption techniques......Page 321
10.6. Determination of chemical composition and atomic densities by absorption techniques......Page 327
Problems......Page 334
References......Page 336
General references and further reading......Page 337
11.1. Introduction......Page 338
11.2. Population inversion and the atomic gain coefficient......Page 340
11.3. Transient and steady state population inversion......Page 344
11.4. Population inversion mechanisms in gas lasers......Page 348
Problems......Page 370
References......Page 372
General references and further reading......Page 373
12.1. Introduction......Page 374
12.2. Numerical solution of cavity mode problem......Page 375
12.3. Approximate analytic solutions for transverse modes......Page 380
12.4. Mode size and cavity stability......Page 384
12.5. Design considerations for practical systems......Page 387
12.6. Cavity Q-factor and resonance linewidth......Page 389
Problems......Page 391
References......Page 394
General references and further reading......Page 395
13. SATURATION CHARACTERISTICS AND SINGLE-FREQUENCY OPERATION OF GAS LASERS......Page 396
13.1. Frequencies of the resonant cavity modes......Page 397
13.2. Gain required for oscillation......Page 400
13.3. Gain saturation : homogeneously-broadened transitions......Page 402
13.4. Gain saturation : inhomogeneously-broadened transitions......Page 407
13.5. Measurement of gain coefficients......Page 415
13.6. Mode-locking of gas lasers......Page 418
13.7. Single-frequency operation of gas lasers......Page 421
13.8. Output power versus tuning curves for single-frequency gas lasers......Page 428
13.9. Saturated absorption spectroscopy using tunable gas lasers......Page 433
13.10. Frequency stabilization of single-frequency gas lasers......Page 439
Problems......Page 451
References......Page 455
General references and further reading......Page 457
14.1. Introduction......Page 458
14.2. Tunable organic dye lasers......Page 459
14.3. Saturated absorption spectroscopy using tunable dye lasers......Page 473
14.4. Two-photon absorption spectrescopy......Page 481
References......Page 489
General references and further reading......Page 490
15. THE HANLE EFFECT AND THE THEORY OF RESONANCE FLUORESCENCE EXPERIMENTS......Page 492
15.1. Resonance radiation and resonance fluorescence......Page 493
15.2. Magnetic depolarization of resonance radiation the Hanle effect......Page 496
15.3. Excitation by electron impact......Page 504
15.4. Range and accuracy of lifetime measurements......Page 510
15.5. Theory of resonance fluorescence experiments......Page 511
15.6. Theory of the Hanle effect......Page 520
15.7. Theory of resonance fluorescence in the J[sub(e)] = 1↔J[sub(g)] = 0 case......Page 525
15.8. Resonance fluorescence experiments using pulsed excitation......Page 531
15.9. Resonance fluorescence experiments using modulated excitation......Page 539
Problems......Page 545
References......Page 549
General references and further reading......Page 551
16.1. Magnetic resonance and excited atoms......Page 553
16.2. Theory of the Brossel-Bitter experiment......Page 558
16.3. Discussion of the optical double-resonance method......Page 567
16.4. Radiation trapping and coherence narrowing......Page 571
16.5. Collision broadening in resonance fluorescence experiments......Page 576
16.6. Light modulation in double-resonance experiments......Page 591
16.7. Magnetic resonance in the density matrix formalism......Page 595
16.8. Expansion of the density matrix in terms of irreducible tensor operators......Page 603
Problems......Page 605
References......Page 608
General references and further reading......Page 609
17.1. Introduction......Page 611
17.2. Principles of optical pumping......Page 612
17.3. Effect of relaxation processes......Page 620
17.4. Investigation of longitudinal relaxation times......Page 623
17.5. Spin-exchange collisions......Page 632
17.6. Optical pumping of metastable atoms......Page 635
17.7. Optical pumping and magnetic resonance......Page 638
17.8. Transverse magnetization and Hertzian coherence in optical pumping experiments......Page 648
17.9. Quantum theory of the optical pumping cycle......Page 658
Problems......Page 673
References......Page 677
General references and further reading......Page 678
18. THE HYPERFINE STRUCTURE OF ATOMS AND ITS INVESTIGATION BY MAGNETIC RESONANCE METHODS......Page 680
18.1. Theory of hyperfine structure......Page 681
18.2. Investigation of hyperfine structure of ground-state atoms by optical pumping......Page 695
18.3. Hyperfine pumping and the measurement of v[sub(HFS)]......Page 701
18.4. Optically pumped rubidium frequency standards......Page 708
18.5. The atomic beam magnetic resonance technique......Page 711
18.6. Hyperfine structure investigations by the atomic beam technique......Page 720
18.7. Cesium beam atomic clock......Page 724
18.8. Hyperfine structure of atomic hydrogen......Page 727
18.9. Investigation of the hyperfine structure of excited states......Page 733
18.10. Conclusion......Page 749
Problems......Page 750
References......Page 757
General references and further reading......Page 759
APPENDIX: TABLE OF FUNDAMENTAL CONSTANTS......Page 761
B......Page 764
C......Page 765
F......Page 766
H......Page 767
L......Page 768
N......Page 769
S......Page 770
T......Page 771
Z......Page 772
B......Page 773
D......Page 774
F......Page 775
H......Page 776
L......Page 777
M......Page 778
O......Page 779
R......Page 780
T......Page 781
Z......Page 782