Neskovic / Neškovic / Petrovic Rainbows in Channeling of Charged Particles in Crystals and Nanotubes

1. Auflage 2017
ISBN: 978-3-319-61524-0
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 25, 202 Seiten

Reihe: Lecture Notes in Nanoscale Science and Technology

This book discusses the effects, modeling, latest results, and nanotechnology applications of rainbows that appear during channeling of charged particles in crystals and nanotubes. The authors begin with a brief review of the optical and particle rainbow effects followed by a detailed description of crystal rainbows, which appear in ion channeling in crystals, and their modeling using catastrophe theory. The effects of spatial and angular focusing of channeled ions are described, with special attention given to the applications of the former effect to subatomic microscopy. The results of a thorough study of the recent high-resolution channeling experiments performed with protons of energies between 2.0 and 0.7 MeV and a 55 nm thick silicon crystal are also provided. This study opens up the potential for accurate analysis of very thin crystals. Also presented are recent results related to rainbows occurring in proton transmission through carbon nanotubes, and a detailed quantum consideration of the transmission of positrons of an energy of 1 MeV through very short carbon nanotubes. This process is determined by the rainbow effect. The initial positron beam is represented as an ensemble of non-interacting Gaussian wave packets, and the principal and supernumerary primary rainbows appearing in the spatial and angular distributions of transmitted positrons are clearly identified. They are explained by the effects of wrinkling, concentration and coordination of the wave packets.

Autoren/Hrsg.

Neskovic, Nebojsa

Neškovic, Nebojša

Petrovic, Srdjan

Cosic, Marko

Inhaltsverzeichnis

1;Prologue;5
2;Contents;8
3;Chapter 1: Rainbows;10
3.1;1.1 Optical Rainbows;11
3.2;1.2 Particle Rainbows;16
3.2.1;1.2.1 Atomic Rainbows;16
3.2.2;1.2.2 Coulomb and Nuclear Rainbows;17
3.2.3;1.2.3 Surface Rainbows;20
3.2.4;1.2.4 Crystal Rainbows;23
4;Chapter 2: Ion Channeling;24
4.1;2.1 Basic Facts;24
4.2;2.2 Interaction Potentials;25
4.3;2.3 Computer Simulations;27
4.3.1;2.3.1 Applicability of Classical Mechanics;27
4.3.2;2.3.2 Continuum String Model;28
4.3.3;2.3.3 Binary Collision Model;31
5;Chapter 3: Crystal Rainbows;33
5.1;3.1 Ion Channeling in Very Thin Crystals;33
5.1.1;3.1.1 Model of Crystal Rainbows;33
5.1.2;3.1.2 First Measurements of the Crystal Rainbows;41
5.2;3.2 Crystal Rainbows as Elementary Catastrophes;48
5.2.1;3.2.1 Crystal Rainbow Effect as a Catastrophic Effect;48
5.2.2;3.2.2 The 4X9 Catastrophe as the Organizing Center of Crystal Rainbows;55
5.3;3.3 Zero-Degree Focusing Effect;67
5.4;3.4 Theory of Crystal Rainbows;72
6;Chapter 4: Rainbows in Proton Channeling in Silicon Crystals;81
6.1;4.1 Rainbow Interaction Potentials;82
6.1.1;4.1.1 High-Resolution Measurements of the Crystal Rainbows;82
6.1.2;4.1.2 Interaction Potentials;83
6.1.3;4.1.3 Morphological Method of Extraction of the Interaction Potentials;83
6.2;4.2 Inverse Transmission;93
6.3;4.3 Superfocusing Effect;98
6.3.1;4.3.1 Axial Focusing;98
6.3.2;4.3.2 Rainbow Subatomic Microscopy;104
6.3.3;4.3.3 Measurement of the Superfocusing Effect;116
6.4;4.4 Doughnut Effect;117
6.4.1;4.4.1 Explanation of the Doughnut Effect;117
6.4.2;4.4.2 High-Resolution Measurement of the Doughnut Effect;122
7;Chapter 5: Rainbows with Protons and Carbon Nanotubes;127
7.1;5.1 Rainbows with a Straight Very Short Bundle of Nanotubes;129
7.1.1;5.1.1 Zero-Degree Focusing Effect;129
7.1.2;5.1.2 Rainbow Effect;132
7.2;5.2 Spatial and Angular Rainbows with a Bent Very Short Nanotube;136
7.2.1;5.2.1 Spatial and Angular Distributions;136
7.2.2;5.2.2 Spatial and Angular Rainbows;141
7.3;5.3 Spatial and Angular Rainbows with Straight Very Long Nanotubes;146
7.3.1;5.3.1 Spatial Rainbow Effect;150
7.3.2;5.3.2 Angular Rainbow Effect;154
7.3.3;5.3.3 Trajectories;158
8;Chapter 6: Rainbows with Positrons and Carbon Nanotubes;161
8.1;6.1 Quantum Mechanical Theory of Rainbow Channeling;162
8.1.1;6.1.1 Interaction Potentials;162
8.1.2;6.1.2 Classical Approach;164
8.1.3;6.1.3 Quantum Mechanical Approach;166
8.2;6.2 Spatial and Angular Primary Rainbows;167
8.2.1;6.2.1 Classical Rainbows;167
8.2.2;6.2.2 Quantum Rainbows;170
8.2.2.1;6.2.2.1 Quantum Spatial Primary Rainbows for L = 50 nm;171
8.2.2.2;6.2.2.2 Quantum Spatial Primary Rainbows for L = 100 nm;177
8.2.2.3;6.2.2.3 Quantum Angular Primary Rainbows for L = 250 nm;181
9;Epilogue;187
10;References;189
11;Author Index;199
12;Subject Index;201