 | Demtröder W. Atoms, molecules and photons: an introduction to atomic-, molecular- and quantum physics. - 2nd ed. - Berlin, Heidelberg: Springer, 2010. - vii, 589 p.: ill. - (Graduate texts in physics). - Ref.: p.571-589. - Sub. ind.: p.581-589. - ISBN 978-3-642-10297-4
|
1 Introduction ................................................. 1
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 ...................................... 7
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 .............................. 81
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 ........................ 129
4.1 The Schrodinger 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 .......................................... 159
5.1 Schrodinger 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 Schrodinger 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 .......................... 201
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 ...................................................... 248
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
8 Lasers ..................................................... 289
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 ......................................... 327
9.1 The Molecular Ion ..................................... 327
9.1.1 The Exact Solution for the Rigid H2+
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 ....................................... 383
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 .... 422
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 ........ 487
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 Schrodinger'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
|
|
