Nonrelativistic Quantum XRay PhysicsISBN: 9783527411603
320 pages
January 2015

Description
The text presupposes a basic (undergraduatelevel) understanding of mechanics, electrodynamics, and quantum mechanics. However, more specialized concepts in these fields are introduced and the reader is directed to appropriate references. While primarily benefiting users of xray lightsources, the material is equally of relevance to researchers in various disciplines, such as life sciences, biology, materials science, physics, and chemistry that plan on applying these new facilities in their respective fields.
Table of Contents
Preface XIII
Part I Introduction 1
1 Introduction 3
1.1 Motivation 3
1.2 Comparing XRays with Optical Radiation 3
1.3 Novel XRay Sources 5
1.4 Unit Systems 6
1.5 Overview of Lagrangian and Hamiltonian Mechanics 9
1.5.1 Lagrangian Mechanics 9
1.5.2 Hamiltonian Mechanics 10
1.6 Approximations 12
1.6.1 Semiclassical Approximation 12
1.6.2 Dipole Approximation 13
2 Review of Some Concepts in Quantum Mechanics 15
2.1 Introduction 15
2.2 Dirac’s Bra–Ket (Bracket) Notation 15
2.3 Eigenvalues and Eigenfunctions 16
2.4 Functions of Operators 18
2.5 Point Particle in a Radially Symmetric Potential 19
2.5.1 Radial Schrödinger Equation 19
2.5.2 Bound States in a Modified Attractive Coulomb Potential 21
2.5.3 Unbound States in a Coulomb Potential 21
2.5.4 Pure Coulomb Potential 22
2.6 Mixed States 23
2.6.1 Isolated Systems 23
2.6.2 Coupled Systems 25
2.7 Schrödinger and Heisenberg Pictures of Quantum Mechanics 26
2.7.1 Evolution Operator in the Schrödinger Picture 26
2.7.2 Equivalent Pictures of Quantum Mechanics 28
2.7.3 Schrödinger Picture 28
2.7.4 Heisenberg Picture 29
2.8 Representing Quantum Mechanics in Position and Momentum Space 29
2.9 Transition from Classical Mechanics to Quantum Mechanics 31
2.10 Molecular Orbital Approximation 31
2.10.1 Derivation of the Hartree–Fock Equations 32
2.10.2 Interpretation of Orbital Energies 38
2.10.3 PostHartree–Fock Methods 40
Part II Quantization of the Free Electromagnetic Field 41
3 Classical Electromagnetic Fields 43
3.1 Introduction 43
3.2 Maxwell’s Equations 43
3.3 Electromagnetic Potentials 44
3.3.1 Field Equations 44
3.3.2 Gauge Transformation 45
3.3.3 Coulomb Gauge 45
3.3.4 Lorenz Gauge 46
3.4 Transverse and Longitudinal Maxwell’s Equations 46
3.4.1 Helmholtz Decomposition of Maxwell’s Equations 47
3.4.2 Decomposition of the Field Equations in the Coulomb Gauge 47
3.5 The Free Electromagnetic Field as a Sum of Mode Oscillators 48
3.5.1 Density of States of the Radiation Field 53
3.5.2 Radiation Cavity in Thermodynamic Equilibrium 54
3.6 Charged Particle in an Electromagnetic Field and the MinimalCoupling Hamiltonian 56
4 Harmonic Oscillator 59
4.1 Introduction 59
4.2 Classical Harmonic Oscillator with One Degree of Freedom 59
4.3 Quantum Mechanical Harmonic Oscillator 60
4.4 NDimensional Quantum Mechanical Harmonic Oscillator 64
5 Quantization of the Electromagnetic Field 67
5.1 Introduction 67
5.2 Transition to a Quantum Mechanical Description 67
5.3 Photon Number States (Fock States) 71
5.4 Photons 73
5.4.1 Photon Momentum and Poynting Vector 73
6 Continuous Fock Space 77
6.1 Introduction 77
6.2 ThreeDimensional Continuum Field 77
6.2.1 Number States in the Continuum Field 80
6.3 OneDimensional Treatment 84
6.3.1 Intensity 85
6.3.2 Description in the Time Domain 86
7 Coherence 89
7.1 Introduction 89
7.2 Review of Classical Coherence Theory 89
7.2.1 FirstOrder Coherence 90
7.2.2 SecondOrder Coherence 92
7.2.3 Chaotic Light 93
7.3 Quantum Coherence Theory 96
7.3.1 Coincidence Detection Using an Ideal Photon Detector 96
7.3.2 Field Correlations 98
7.3.3 Coherence 101
8 Examples for Electromagnetic States 103
8.1 Introduction 103
8.2 Quantum Phase of Radiation Fields 103
8.2.1 Dirac’s Phase Operator 104
8.2.2 Quantum Sine and Cosine Operators 105
8.2.3 Phase State Projectors 108
8.3 SingleMode States 109
8.3.1 Pure SingleMode States 110
8.3.2 Statistical Mixtures of SingleMode States 112
8.3.3 Coherent States 113
8.4 Multimode States 117
8.4.1 Multimode Fock States 117
8.4.2 Multimode Coherent States 119
8.4.3 Localized Radiation (Wave Packets Describing Localized Photons) 120
8.4.4 Chaotic Light 123
8.5 OneDimensional Continuum Mode States 124
Part III Interaction of XRays with Matter 125
9 Interaction of the Electromagnetic Field with Matter 127
9.1 Introduction 127
9.2 Tensor Product of Matter and Radiation Hilbert Spaces 127
9.3 Interaction Hamiltonian for the Electromagnetic Field and Matter 128
10 TimeDependent Perturbation Theory 133
10.1 Introduction 133
10.2 Interaction Picture 134
10.2.1 Pure States 134
10.2.2 Mixed States 136
10.3 Transition Probabilities 137
10.3.1 Time Dependence of Perturbations 137
10.3.2 Transition Probabilities 139
10.4 Perturbative Expansion of Transition Amplitudes 141
10.4.1 Transition Amplitude in First Order 144
10.4.2 Transition Amplitude in Second Order 145
10.4.3 Transition Between Discrete States 148
10.4.4 Transition from Discrete to Continuous States 149
10.4.5 Transition Between Continuous States 152
10.4.6 Scattering (̂S) and Transition ( ̂ T) Matrices 153
10.5 TimeDependent Perturbation Theory for Mixed States 154
10.5.1 Isolated System 154
10.5.2 Coupled Systems 155
11 Application of Perturbation Theory to the Interaction of Electromagnetic Fields with Matter 159
11.1 Introduction 159
11.2 Feynman Diagrams 160
11.3 Mixed States 161
11.3.1 Transition Probabilities 162
Part IV Applications of XRay–MatterInteraction Theory 165
12 XRay Scattering by Free Electrons 167
12.1 Introduction 167
12.2 Energy and Momentum Conservation 167
12.2.1 Scattering of Photons by Free Electrons 167
12.2.2 A Free Electron Cannot Absorb a Photon 170
12.3 Scattering Cross Section 171
12.4 Scattering From an Electron at Rest 176
12.4.1 Kinematics 176
12.4.2 Nonrelativistic Scattering Cross Section 177
12.4.3 Polarization 178
12.4.4 Relativistic Klein–Nishima Cross Section 179
12.5 Doppler Effect 179
13 Radiative Atomic Bound–Bound Transitions 183
13.1 Introduction 183
13.2 Emission of Photons 183
13.3 Lifetime and Natural Line Width 187
13.3.1 Weisskopf–Wigner Theory 187
13.3.2 Frequency Spectrum 191
13.3.3 Breit–Wigner Procedure 191
13.4 Absorption of Photons 192
13.5 Einstein’s A and B Coefficients 194
13.6 Radiative Atomic Bound–Bound Transitions in Mixed States 197
14 OnePhoton Photoionization 201
14.1 Introduction 201
14.2 Photoionization in a PureState Radiation Field 201
14.3 Photoionization in a MixedState Radiation Field 204
14.4 SingleElectron Approximation for Photoionization 207
14.5 Photoionization of HydrogenLike Atoms 210
14.5.1 Large Photon Energies 211
14.5.2 Small Photon Energies 214
14.5.3 Comparing Small and Large Photon Energies 217
15 Bremsstrahlung 221
15.1 Introduction 221
15.2 Electron–Nucleus Bremsstrahlung 221
15.3 Electron–Positron Bremsstrahlung 225
15.4 Electron–Electron Bremsstrahlung 229
15.4.1 Quadrupole Nature of Bremsstrahlung 229
15.4.2 Indistinguishable Particles 230
15.5 Inverse Bremsstrahlung Absorption 231
16 XRay Scattering 235
16.1 Introduction 235
16.2 SteadyState Scattering Formalism 236
16.2.1 Dipole Approximation 241
16.3 Elastic Scattering (Rayleigh Scattering) 241
16.3.1 Elastic Scattering for Large XRay Energies 242
16.3.2 Elastic Scattering for Intermediate XRay Energies 243
16.4 Raman Scattering 244
16.5 Compton Scattering 246
16.5.1 Nonresonant Compton Scattering 247
16.5.2 Resonant Raman–Compton Scattering 252
16.5.3 Infrared Divergence for Soft Scattered Photon Energies 252
16.6 SingleElectron Approximation for XRay Scattering 253
16.7 ShortPulse Scattering 255
16.7.1 General Formalism 256
16.7.2 PlaneParallel Light Pulse 260
16.7.3 Coherent Pulses 261
17 Relaxation Processes 265
17.1 Introduction 265
17.2 Auger Decay 266
17.2.1 Eigenstates Due to Coupling of a Discrete Level to a Continuum 266
17.2.2 Autoionization in FirstOrder Perturbation Theory 269
17.3 XRay Fluorescence following Photoionization 271
17.4 Branching Ratio 274
18 Multiphoton Photoionization 277
18.1 Introduction 277
18.2 AboveThreshold Ionization 278
18.3 Sequential TwoPhoton Absorption 279
19 Threshold Phenomena 285
19.1 Introduction 285
19.2 OneStep Treatment of Threshold Excitations 286
19.3 Nonradiative Threshold Processes 288
19.3.1 ShakeModified Resonant Autoionization 289
19.3.2 PostCollision Interaction 289
References 293
Index 299