Atoms, Molecules and Photons,Demtroder. W, 2005. publisher: Springer FREE PDF DOWNLOAD

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CONTENTS

1. Introduction
1.1 Contents and Importance of Atomic Physics . . . . . . . . . . . 1
1.2 Molecules: Building Blocks of Nature . . . . . . . . . . . . . . . 3
1.3 Survey on the Concept of this Textbook . . . . . . . . . . . . . . 4
2. The Concept of the Atom
2.1 Historical Development . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Experimental and Theoretical Proofs for the Existence
of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Dalton’s Law of Constant Proportions . . . . . . . . . 9
2.2.2 The Law of Gay-Lussac and the Definition
of the Mole . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Experimental Methods for the Determination
of Avogadro’s Constant . . . . . . . . . . . . . . . . . 12
2.2.4 The Importance of Kinetic Gas Theory
for the Concept of Atoms . . . . . . . . . . . . . . . . 17
2.3 Can One See Atoms? . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Brownian Motion . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Cloud Chamber . . . . . . . . . . . . . . . . . . . . . 24
2.3.3 Microscopes with Atomic Resolution . . . . . . . . . . 24
2.4 The Size of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.1 The Size of Atoms in the Van der Waals
Equation . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.2 Atomic Size Estimation from Transport
Coefficients . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.3 Atomic Volumes from X-Ray Diffraction . . . . . . . . 31
2.4.4 Comparison of the Different Methods . . . . . . . . . . 32
2.5 The Electric Structure of Atoms . . . . . . . . . . . . . . . . . . 33
2.5.1 Cathode Rays and Kanalstrahlen . . . . . . . . . . . . 34
2.5.2 Measurement of the Elementary Charge e . . . . . . . 35
2.5.3 How to Produce Free Electrons . . . . . . . . . . . . . 37
2.5.4 Generation of Free Ions . . . . . . . . . . . . . . . . . 39
2.5.5 The Mass of the Electron . . . . . . . . . . . . . . . . 41
2.5.6 How Neutral is the Atom? . . . . . . . . . . . . . . . . 44
2.6 Electron and Ion Optics . . . . . . . . . . . . . . . . . . . . . . 45
2.6.1 Refraction of Electron Beams . . . . . . . . . . . . . . 45
2.6.2 Electron Optics in Axially Symmetric Fields . . . . . . 47
2.6.3 Electrostatic Electron Lenses . . . . . . . . . . . . . . 49
2.6.4 Magnetic Lenses . . . . . . . . . . . . . . . . . . . . . 50
2.6.5 Applications of Electron and Ion Optics . . . . . . . . 52
2.7 Atomic Masses and Mass Spectrometers . . . . . . . . . . . . . 53
2.7.1 J.J. Thomson’s Parabola Spectrograph . . . . . . . . . 54
2.7.2 Velocity-Independent Focusing . . . . . . . . . . . . . 55
2.7.3 Focusing of Ions with Different Angles
of Incidence . . . . . . . . . . . . . . . . . . . . . . . 57
2.7.4 Mass Spectrometer with Double Focusing . . . . . . . 57
2.7.5 Time-of-Flight Mass Spectrometer . . . . . . . . . . . 58
2.7.6 Quadrupole Mass Spectrometer . . . . . . . . . . . . . 61
2.7.7 Ion-Cyclotron-Resonance Spectrometer . . . . . . . . 63
2.7.8 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.8 The Structure of Atoms . . . . . . . . . . . . . . . . . . . . . . 65
2.8.1 Integral and Differential Cross Sections . . . . . . . . . 65
2.8.2 Basic Concepts of Classical Scattering . . . . . . . . . 66
2.8.3 Determination of the Charge Distribution
within the Atom from Scattering Experiments . . . . . 70
2.8.4 Thomson’s Atomic Model . . . . . . . . . . . . . . . . 71
2.8.5 The Rutherford Atomic Model . . . . . . . . . . . . . 73
2.8.6 Rutherford’s Scattering Formula . . . . . . . . . . . . 74
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3. Development of Quantum Physics
3.1 Experimental Hints to the Particle Character
of Electromagnetic Radiation . . . . . . . . . . . . . . . . . . . 81
3.1.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . 82
3.1.2 Cavity Modes . . . . . . . . . . . . . . . . . . . . . . . 84
3.1.3 Planck’s Radiation Law . . . . . . . . . . . . . . . . . 86
3.1.4 Wien’s Law . . . . . . . . . . . . . . . . . . . . . . . . 88
3.1.5 Stefan–Boltzmann’s Radiation Law . . . . . . . . . . . 88
3.1.6 Photoelectric Effect . . . . . . . . . . . . . . . . . . . 89
3.1.7 Compton Effect . . . . . . . . . . . . . . . . . . . . . . 91
3.1.8 Properties of Photons . . . . . . . . . . . . . . . . . . . 93
3.1.9 Photons in Gravitational Fields . . . . . . . . . . . . . 94
3.1.10 Wave and Particle Aspects of Light . . . . . . . . . . . 95
3.2 Wave Properties of Particles . . . . . . . . . . . . . . . . . . . . 97
3.2.1 De Broglie Wavelength and Electron Diffraction . . . . 97
3.2.2 Diffraction and Interference of Atoms . . . . . . . . . . 98
3.2.3 Bragg Reflection and the Neutron Spectrometer . . . . . 100
3.2.4 Neutron and Atom Interferometry . . . . . . . . . . . . 100
3.2.5 Application of Particle Waves . . . . . . . . . . . . . . 101
3.3 Matter Waves and Wave Functions . . . . . . . . . . . . . . . . . 102
3.3.1 Wave Packets . . . . . . . . . . . . . . . . . . . . . . . 103
3.3.2 The Statistical Interpretation of Wave Functions . . . . 105
3.3.3 Heisenberg’s Uncertainty Principle . . . . . . . . . . . 106
3.3.4 Dispersion of the Wave Packet . . . . . . . . . . . . . . 109
3.3.5 Uncertainty Relation for Energy and Time . . . . . . . 110
3.4 The Quantum Structure of Atoms . . . . . . . . . . . . . . . . . 111
3.4.1 Atomic Spectra . . . . . . . . . . . . . . . . . . . . . . 112
3.4.2 Bohr’s Atomic Model . . . . . . . . . . . . . . . . . . 113
3.4.3 The Stability of Atoms . . . . . . . . . . . . . . . . . . 117
3.4.4 Franck–Hertz Experiment . . . . . . . . . . . . . . . . 118
3.5 What are the Differences Between Classical
and Quantum Physics? . . . . . . . . . . . . . . . . . . . . . 120
3.5.1 Classical Particle Paths Versus Probability
Densities in Quantum Physics . . . . . . . . . . . . . . 120
3.5.2 Interference Phenomena with Light Waves
and Matter Waves . . . . . . . . . . . . . . . . . . . . 121
3.5.3 The Effect of the Measuring Process . . . . . . . . . . . 123
3.5.4 The Importance of Quantum Physics
for our Concept of Nature . . . . . . . . . . . . . . . . 124
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4. Basic Concepts of Quantum Mechanics
4.1 The Schrödinger Equation . . . . . . . . . . . . . . . . . . . . . 129
4.2 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.2.1 The Free Particle . . . . . . . . . . . . . . . . . . . . . 131
4.2.2 Potential Barrier . . . . . . . . . . . . . . . . . . . . . 132
4.2.3 Tunnel Effect . . . . . . . . . . . . . . . . . . . . . . . 135
4.2.4 Particle in a Potential Box . . . . . . . . . . . . . . . . 138
4.2.5 Harmonic Oscillator . . . . . . . . . . . . . . . . . . . 141
4.3 Two-and Three-Dimensional Problems . . . . . . . . . . . . . . 144
4.3.1 Particle in a Two-dimensional Box . . . . . . . . . . . . 144
4.3.2 Particle in a Spherically Symmetric Potential . . . . . . 145
4.4 Expectation Values and Operators . . . . . . . . . . . . . . . . . 149
4.4.1 Operators and Eigenvalues . . . . . . . . . . . . . . . . 150
4.4.2 Angular Momentum in Quantum Mechanics . . . . . . 152
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5. The Hydrogen Atom
5.1 Schrödinger Equation for One-electron Systems . . . . . . . . . 159
5.1.1 Separation of the Center of Mass
and Relative Motion . . . . . . . . . . . . . . . . . . . 159
5.1.2 Solution of the Radial Equation . . . . . . . . . . . . . 161
5.1.3 Quantum Numbers and Wave Functions
of the H Atom . . . . . . . . . . . . . . . . . . . . . . 163
5.1.4 Spatial Distributions and Expectation Values
of the Electron in Different Quantum States . . . . . . . 166
5.2 The Normal Zeeman Effect . . . . . . . . . . . . . . . . . . . . 168
5.3 Comparison of Schrödinger Theory with Experimental Results . . 170
5.4 Relativistic Correction of Energy Terms . . . . . . . . . . . . . . 172
5.5 The Electron Spin . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.5.1 The Stern–Gerlach Experiment . . . . . . . . . . . . . 175
5.5.2 Experimental Confirmation of Electron Spin . . . . . . 176
5.5.3 Einstein–de Haas Effect . . . . . . . . . . . . . . . . . 177
5.5.4 Spin-Orbit Coupling and Fine Structure . . . . . . . . . 178
5.5.5 Anomalous Zeeman Effect . . . . . . . . . . . . . . . 181
5.6 Hyperfine Structure . . . . . . . . . . . . . . . . . . . . . . . . 184
5.6.1 Basic Considerations . . . . . . . . . . . . . . . . . . . 184
5.6.2 Fermi-contact Interaction . . . . . . . . . . . . . . . . 186
5.6.3 Magnetic Dipole-Dipole Interaction . . . . . . . . . . . 187
5.6.4 Zeeman Effect of Hyperfine Structure Levels . . . . . . 187
5.7 Complete Description of the Hydrogen Atom . . . . . . . . . . . 188
5.7.1 Total Wave Function and Quantum Numbers . . . . . . 188
5.7.2 Term Assignment and Level Scheme . . . . . . . . . . 188
5.7.3 Lamb Shift . . . . . . . . . . . . . . . . . . . . . . . . 191
5.8 Correspondence Principle . . . . . . . . . . . . . . . . . . . . . 194
5.9 The Electron Model and its Problems . . . . . . . . . . . . . . . 195
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6. Atoms with More Than One Electron
6.1 The Helium Atom . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.1.1 Approximation Models . . . . . . . . . . . . . . . . . 202
6.1.2 Symmetry of the Wave Function . . . . . . . . . . . . 203
6.1.3 Consideration of the Electron Spin . . . . . . . . . . . 204
6.1.4 The Pauli Principle . . . . . . . . . . . . . . . . . . . 205
6.1.5 Energy Levels of the Helium Atom . . . . . . . . . . . 206
6.1.6 Helium Spectrum . . . . . . . . . . . . . . . . . . . . 208
6.2 Building-up Principle of the Electron Shell for Larger Atoms . . 209
6.2.1 The Model of Electron Shells . . . . . . . . . . . . . . 209
6.2.2 Successive Building-up of Electron Shells
for Atoms with Increasing Nuclear Charge . . . . . . . 210
6.2.3 Atomic Volumes and Ionization Energies . . . . . . . . 212
6.2.4 The Periodic System of the Elements . . . . . . . . . . 216
6.3 Alkali Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
6.4 Theoretical Models for Multielectron Atoms . . . . . . . . . . . 221
6.4.1 The Model of Independent Electrons . . . . . . . . . . 221
6.4.2 The Hartree Method . . . . . . . . . . . . . . . . . . . 222
6.4.3 The Hartree–Fock Method . . . . . . . . . . . . . . . . 224
6.4.4 Configuration Interaction . . . . . . . . . . . . . . . . 224
6.5 Electron Configurations and Couplings of Angular Momenta . . . 224
6.5.1 Coupling Schemes for Electronic
Angular Momenta . . . . . . . . . . . . . . . . . . . . 224
6.5.2 Electron Configuration and Atomic States . . . . . . . 229
6.6 Excited Atomic States . . . . . . . . . . . . . . . . . . . . . . . 231
6.6.1 Single Electron Excitation . . . . . . . . . . . . . . . . 232
6.6.2 Simultaneous Excitation of Two Electrons . . . . . . . 232
6.6.3 Inner-Shell Excitation and the Auger Process . . . . . . 233
6.6.4 Rydberg States . . . . . . . . . . . . . . . . . . . . . . 234
6.6.5 Planetary Atoms . . . . . . . . . . . . . . . . . . . . . 236
6.7 Exotic Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
6.7.1 Muonic Atoms . . . . . . . . . . . . . . . . . . . . . . 238
6.7.2 Pionic and Kaonic Atoms . . . . . . . . . . . . . . . . 239
6.7.3 Anti-hydrogen Atoms and Other Anti-atoms . . . . . . 240
6.7.4 Positronium and Muonium . . . . . . . . . . . . . . . 241
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
7. Emission and Absorption of Electromagnetic Radiation by Atoms
7.1 Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . . 248
7.1.1 Induced and Spontaneous Transitions,
Einstein Coefficients . . . . . . . . . . . . . . . . . . . 248
7.1.2 Transition Probabilities, Einstein Coefficients
and Matrix Elements . . . . . . . . . . . . . . . . . . . 250
7.1.3 Transition Probabilities for Absorption
and Induced Emission . . . . . . . . . . . . . . . . . . 253
7.2 Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
7.2.1 Selection Rules for Spontaneous Emission . . . . . . . 253
7.2.2 Selection Rules for the Magnetic Quantum Number . . 254
7.2.3 Parity Selection Rules . . . . . . . . . . . . . . . . . . 255
7.2.4 Selection Rules for Induced Absorption and Emission . 256
7.2.5 Selection Rules for the Spin Quantum Number . . . . . 256
7.2.6 Higher Order Multipole Transitions . . . . . . . . . . . 257
7.2.7 Magnetic Dipole Transitions . . . . . . . . . . . . . . . 259
7.2.8 Two-Photon-Transitions . . . . . . . . . . . . . . . . . 259
7.3 Lifetimes of Excited States . . . . . . . . . . . . . . . . . . . . . 260
7.4 Line Profiles of Spectral Lines . . . . . . . . . . . . . . . . . . . 261
7.4.1 Natural Linewidth . . . . . . . . . . . . . . . . . . . . 262
7.4.2 Doppler Broadening . . . . . . . . . . . . . . . . . . . 264
7.4.3 Collision Broadening . . . . . . . . . . . . . . . . . . . 267
7.5 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
7.5.1 Bremsstrahlung . . . . . . . . . . . . . . . . . . . . . . 271
7.5.2 Characteristic X-Ray-Radiation . . . . . . . . . . . . . 272
7.5.3 Scattering and Absorption of X-Rays . . . . . . . . . . 273
7.5.4 X-ray Fluorescence . . . . . . . . . . . . . . . . . . . . 278
7.5.5 Measurements of X-Ray Wavelengths . . . . . . . . . . 278
7.6 Continuous Absorption and Emission Spectra . . . . . . . . . . . 280
7.6.1 Photoionization . . . . . . . . . . . . . . . . . . . . . . 281
7.6.2 Recombination Radiation . . . . . . . . . . . . . . . . 284
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
XIV Contents
8. Lasers
8.1 Physical Principles . . . . . . . . . . . . . . . . . . . . . . . . . 289
8.1.1 Threshold Condition . . . . . . . . . . . . . . . . . . . 290
8.1.2 Generation of Population Inversion . . . . . . . . . . . 292
8.1.3 The Frequency Spectrum of Induced Emission . . . . . 295
8.2 Optical Resonators . . . . . . . . . . . . . . . . . . . . . . . . . 295
8.2.1 The Quality Factor of Resonators . . . . . . . . . . . . 295
8.2.2 Open Optical Resonators . . . . . . . . . . . . . . . . 296
8.2.3 Modes of Open Resonators . . . . . . . . . . . . . . . 297
8.2.4 Diffraction Losses of Open Resonators . . . . . . . . . 300
8.2.5 The Frequency Spectrum of Optical Resonators . . . . 301
8.3 Single Mode Lasers . . . . . . . . . . . . . . . . . . . . . . . . 301
8.4 Different Types of Lasers . . . . . . . . . . . . . . . . . . . . . 304
8.4.1 Solid-state Lasers . . . . . . . . . . . . . . . . . . . . 305
8.4.2 Semiconductor Lasers . . . . . . . . . . . . . . . . . . 307
8.4.3 Dye Lasers . . . . . . . . . . . . . . . . . . . . . . . . 308
8.4.4 Gas Lasers . . . . . . . . . . . . . . . . . . . . . . . . 310
8.5 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 313
8.5.1 Optical Frequency Doubling . . . . . . . . . . . . . . 314
8.5.2 Phase Matching . . . . . . . . . . . . . . . . . . . . . 314
8.5.3 Optical Frequency Mixing . . . . . . . . . . . . . . . . 316
8.6 Generation of Short Laser Pulses . . . . . . . . . . . . . . . . . 316
8.6.1 Q-Switched Lasers . . . . . . . . . . . . . . . . . . . . 316
8.6.2 Mode-Locking of Lasers . . . . . . . . . . . . . . . . 318
8.6.3 Optical Pulse Compression . . . . . . . . . . . . . . . 321
8.6.4 Measurements of Ultrashort Optical Pulses . . . . . . . 322
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
9. Diatomic Molecules
9.1 The H+
2 Molecular Ion . . . . . . . . . . . . . . . . . . . . . . . 327
9.1.1 The Exact Solution for the Rigid H+2 Molecule . . . . . 328
9.1.2 Molecular Orbitals and LCAO Approximations . . . . 331
9.1.3 Improvements to the LCAO ansatz . . . . . . . . . . . 334
9.2 The H2 Molecule . . . . . . . . . . . . . . . . . . . . . . . . . 335
9.2.1 Molecular Orbital Approximation . . . . . . . . . . . . 336
9.2.2 The Heitler–London Method . . . . . . . . . . . . . . 337
9.2.3 Comparison Between the Two Approximations . . . . . 338
9.2.4 Improvements to the Approximations . . . . . . . . . . 339
9.3 Electronic States of Diatomic Molecules . . . . . . . . . . . . . 340
9.3.1 The Energetic Order of Electronic States . . . . . . . . 340
9.3.2 Symmetry Properties of Electronic States . . . . . . . . 341
9.3.3 Electronic Angular Momenta . . . . . . . . . . . . . . 341
9.3.4 Electron Spins, Multiplicity and Fine
Structure Splittings . . . . . . . . . . . . . . . . . . . 343
9.3.5 Electron Configurations and Molecular
Ground States . . . . . . . . . . . . . . . . . . . . . . 344
9.3.6 Excited Molecular States . . . . . . . . . . . . . . . . 346
9.3.7 Excimers . . . . . . . . . . . . . . . . . . . . . . . . . 347
9.3.8 Correlation Diagrams . . . . . . . . . . . . . . . . . . 348
9.4 The Physical Reasons for Molecular Binding . . . . . . . . . . . 349
9.4.1 The Chemical Bond . . . . . . . . . . . . . . . . . . . 349
9.4.2 Multipole Interaction . . . . . . . . . . . . . . . . . . 350
9.4.3 Induced Dipole Moments and van der
Waals Potential . . . . . . . . . . . . . . . . . . . . . 352
9.4.4 General Expansion of the Interaction Potential . . . . . 355
9.4.5 The Morse Potential . . . . . . . . . . . . . . . . . . . 355
9.4.6 Different Binding Types . . . . . . . . . . . . . . . . . 356
9.5 Rotation and Vibration of Diatomic Molecules . . . . . . . . . . 357
9.5.1 The Born-Oppenheimer Approximation . . . . . . . . 357
9.5.2 The Rigid Rotor . . . . . . . . . . . . . . . . . . . . . 359
9.5.3 Centrifugal Distortion . . . . . . . . . . . . . . . . . . 361
9.5.4 The Influence of the Electron Motion . . . . . . . . . . 361
9.5.5 Vibrations of Diatomic Molecules . . . . . . . . . . . . 363
9.5.6 Interaction Between Rotation and Vibration . . . . . . 364
9.5.7 The Dunham Expansion . . . . . . . . . . . . . . . . . 366
9.5.8 Rotational Barrier . . . . . . . . . . . . . . . . . . . . 366
9.6 Spectra of Diatomic Molecules . . . . . . . . . . . . . . . . . . 367
9.6.1 Transition Matrix Elements . . . . . . . . . . . . . . . 367
9.6.2 Vibrational-Rotational Transitions . . . . . . . . . . . 369
9.6.3 The Structure of Electronic Transitions . . . . . . . . . 372
9.6.4 Continuous Spectra . . . . . . . . . . . . . . . . . . . 377
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
10. Polyatomic Molecules
10.1 Electronic States of Polyatomic Molecules . . . . . . . . . . . . 383
10.1.1 The H2O Molecule . . . . . . . . . . . . . . . . . . . 383
10.1.2 Hybridization . . . . . . . . . . . . . . . . . . . . . . 384
10.1.3 The CO2 Molecule . . . . . . . . . . . . . . . . . . . 388
10.1.4 Walsh Diagrams . . . . . . . . . . . . . . . . . . . . . 389
10.2 Molecules with more than Three Atoms . . . . . . . . . . . . . . 390
10.2.1 The NH3 Molecule . . . . . . . . . . . . . . . . . . . 390
10.2.2 Formaldehyde and Other H2AB Molecules . . . . . . . 392
10.2.3 Aromatic Molecules and π-Electron Systems . . . . . . 392
10.3 Rotation of Polyatomic Molecules . . . . . . . . . . . . . . . . . 394
10.3.1 Rotation of Symmetric Top Molecules . . . . . . . . . 397
10.3.2 Asymmetric Rotor Molecules . . . . . . . . . . . . . . 399
10.4 Vibrations of Polyatomic Molecules . . . . . . . . . . . . . . . . 399
10.4.1 Normal Vibrations . . . . . . . . . . . . . . . . . . . . 399
10.4.2 Quantitative Treatment . . . . . . . . . . . . . . . . . 399
10.4.3 Couplings Between Vibrations and Rotations . . . . . . 402
10.5 Spectra of Polyatomic Molecules . . . . . . . . . . . . . . . . . 403
10.5.1 Vibrational Transitions within the Same
Electronic State . . . . . . . . . . . . . . . . . . . . . 404
10.5.2 Rotational Structure of Vibrational Bands . . . . . . . 406
10.5.3 Electronic Transitions . . . . . . . . . . . . . . . . . . 407
10.6 Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
10.6.1 Production of Clusters . . . . . . . . . . . . . . . . . . 410
10.6.2 Physical Properties of Clusters . . . . . . . . . . . . . 410
10.7 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . 412
10.7.1 First Order Reactions . . . . . . . . . . . . . . . . . . 412
10.7.2 Second Order Reactions . . . . . . . . . . . . . . . . . 413
10.7.3 Exothermic and Endothermic Reactions . . . . . . . . 414
10.7.4 Determination of Absolute Reaction Rates . . . . . . . 415
10.8 Molecular Dynamics and Wave Packets . . . . . . . . . . . . . . 416
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
11. Experimental Techniques in Atomic and Molecular Physics
11.1 Basic Principles of Spectroscopic Techniques . . . . . . . . . . . 422
11.2 Spectroscopic Instruments . . . . . . . . . . . . . . . . . . . . . 423
11.2.1 Spectrometers . . . . . . . . . . . . . . . . . . . . . . 423
11.2.2 Interferometers . . . . . . . . . . . . . . . . . . . . . . 429
11.2.3 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 433
11.3 Microwave Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 437
11.4 Infrared Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 440
11.4.1 Infrared Spectrometers . . . . . . . . . . . . . . . . . . 440
11.4.2 Fourier Transform Spectroscopy . . . . . . . . . . . . . 440
11.5 Laser Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 444
11.5.1 Laser-Absorption Spectroscopy . . . . . . . . . . . . . 444
11.5.2 Optoacoustic Spectroscopy . . . . . . . . . . . . . . . 445
11.5.3 Optogalvanic Spectroscopy . . . . . . . . . . . . . . . 447
11.5.4 Cavity-Ringdown Spectroscopy . . . . . . . . . . . . . 448
11.5.5 Laser-Induced Fluorescence Spectroscopy . . . . . . . 450
11.5.6 Ionization Spectroscopy . . . . . . . . . . . . . . . . . 452
11.5.7 Laser Spectroscopy in Molecular Beams . . . . . . . . 453
11.5.8 Nonlinear Laser Spectroscopy . . . . . . . . . . . . . . 455
11.5.9 Saturation Spectroscopy . . . . . . . . . . . . . . . . . 456
11.5.10 Doppler-Free Two-Photon Spectroscopy . . . . . . . . 459
11.6 Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 460
11.6.1 Basic Principles . . . . . . . . . . . . . . . . . . . . . 460
11.6.2 Coherent Anti-Stokes Raman Spectroscopy . . . . . . . 462
11.7 Spectroscopy with Synchrotron Radiation . . . . . . . . . . . . . 463
11.8 Electron Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 465
11.8.1 Experiments on Electron Scattering . . . . . . . . . . . 465
11.8.2 Photoelectron Spectroscopy . . . . . . . . . . . . . . . 467
11.8.3 ZEKE Spectroscopy . . . . . . . . . . . . . . . . . . . 469
11.9 Measurements of Magnetic and Electric Moments
in Atoms and Molecules . . . . . . . . . . . . . . . . . . . . . . 470
11.9.1 The Rabi-Method of Radio-Frequency Spectroscopy . . 471
11.9.2 Stark-Spectroscopy . . . . . . . . . . . . . . . . . . . . 473
11.10 Investigations of Atomic and Molecular Collisions . . . . . . . . 474
11.10.1 Elastic Scattering . . . . . . . . . . . . . . . . . . . . . 475
11.10.2 Inelastic Scattering . . . . . . . . . . . . . . . . . . . . 478
11.10.3 Reactive Scattering . . . . . . . . . . . . . . . . . . . . 479
11.11 Time-Resolved Measurements of Atoms and Molecules . . . . . 480
11.11.1 Lifetime Measurements . . . . . . . . . . . . . . . . . 480
11.11.2 Fast Relaxation Processes in Atoms and Molecules . . . 484
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
12. Modern Developments in Atomic and Molecular Physics
12.1 Optical Cooling and Trapping of Atoms . . . . . . . . . . . . . . 487
12.1.1 Photon Recoil . . . . . . . . . . . . . . . . . . . . . . 487
12.1.2 Optical Cooling of Atoms . . . . . . . . . . . . . . . . 489
12.1.3 Optical Trapping of Atoms . . . . . . . . . . . . . . . . 491
12.1.4 Bose–Einstein Condensation . . . . . . . . . . . . . . . 493
12.1.5 Molecular Spectroscopy in a MOT . . . . . . . . . . . . 495
12.2 Time-resolved Spectroscopy in the Femtosecond Range . . . . . 497
12.2.1 Time-resolved Molecular Vibrations . . . . . . . . . . . 497
12.2.2 Femtosecond Transition State Dynamics . . . . . . . . 498
12.2.3 Coherent Control . . . . . . . . . . . . . . . . . . . . . 499
12.3 Optical Metrology with New Techniques . . . . . . . . . . . . . 501
12.3.1 Frequency Comb . . . . . . . . . . . . . . . . . . . . . 501
12.3.2 Atomic Clocks with Trapped Ions . . . . . . . . . . . . 503
12.4 Squeezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
12.5 New Trends in Quantum Optics . . . . . . . . . . . . . . . . . . 510
12.5.1 Which Way Experiments . . . . . . . . . . . . . . . . . 510
12.5.2 The Einstein–Podolski–Rosen Paradox . . . . . . . . . 512
12.5.3 Schrödinger’s Cat . . . . . . . . . . . . . . . . . . . . 513
12.5.4 Entanglement and Quantum Bits . . . . . . . . . . . . . 513
12.5.5 Quantum Gates . . . . . . . . . . . . . . . . . . . . . . 515
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
Chronological Table for the Development of Atomic
and Molecular Physics . . . . . . . . . . . . . . . . . . . . . . . . . 519
Solutions to the Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581