Rainbows in Channeling of Charged Particles in Crystals and Nanotubes (eBook)

Prologue 5
Contents 8
Chapter 1: Rainbows 10
1.1 Optical Rainbows 11
1.2 Particle Rainbows 16
1.2.1 Atomic Rainbows 16
1.2.2 Coulomb and Nuclear Rainbows 17
1.2.3 Surface Rainbows 20
1.2.4 Crystal Rainbows 23
Chapter 2: Ion Channeling 24
2.1 Basic Facts 24
2.2 Interaction Potentials 25
2.3 Computer Simulations 27
2.3.1 Applicability of Classical Mechanics 27
2.3.2 Continuum String Model 28
2.3.3 Binary Collision Model 31
Chapter 3: Crystal Rainbows 33
3.1 Ion Channeling in Very Thin Crystals 33
3.1.1 Model of Crystal Rainbows 33
3.1.2 First Measurements of the Crystal Rainbows 41
3.2 Crystal Rainbows as Elementary Catastrophes 48
3.2.1 Crystal Rainbow Effect as a Catastrophic Effect 48
3.2.2 The 4X9 Catastrophe as the Organizing Center of Crystal Rainbows 55
3.3 Zero-Degree Focusing Effect 67
3.4 Theory of Crystal Rainbows 72
Chapter 4: Rainbows in Proton Channeling in Silicon Crystals 81
4.1 Rainbow Interaction Potentials 82
4.1.1 High-Resolution Measurements of the Crystal Rainbows 82
4.1.2 Interaction Potentials 83
4.1.3 Morphological Method of Extraction of the Interaction Potentials 83
4.2 Inverse Transmission 93
4.3 Superfocusing Effect 98
4.3.1 Axial Focusing 98
4.3.2 Rainbow Subatomic Microscopy 104
4.3.3 Measurement of the Superfocusing Effect 116
4.4 Doughnut Effect 117
4.4.1 Explanation of the Doughnut Effect 117
4.4.2 High-Resolution Measurement of the Doughnut Effect 122
Chapter 5: Rainbows with Protons and Carbon Nanotubes 127
5.1 Rainbows with a Straight Very Short Bundle of Nanotubes 129
5.1.1 Zero-Degree Focusing Effect 129
5.1.2 Rainbow Effect 132
5.2 Spatial and Angular Rainbows with a Bent Very Short Nanotube 136
5.2.1 Spatial and Angular Distributions 136
5.2.2 Spatial and Angular Rainbows 141
5.3 Spatial and Angular Rainbows with Straight Very Long Nanotubes 146
5.3.1 Spatial Rainbow Effect 150
5.3.2 Angular Rainbow Effect 154
5.3.3 Trajectories 158
Chapter 6: Rainbows with Positrons and Carbon Nanotubes 161
6.1 Quantum Mechanical Theory of Rainbow Channeling 162
6.1.1 Interaction Potentials 162
6.1.2 Classical Approach 164
6.1.3 Quantum Mechanical Approach 166
6.2 Spatial and Angular Primary Rainbows 167
6.2.1 Classical Rainbows 167
6.2.2 Quantum Rainbows 170
6.2.2.1 Quantum Spatial Primary Rainbows for L = 50 nm 171
6.2.2.2 Quantum Spatial Primary Rainbows for L = 100 nm 177
6.2.2.3 Quantum Angular Primary Rainbows for L = 250 nm 181
Epilogue 187
References 189
Author Index 199
Subject Index 201