Relativistic Collisions of Structured Atomic Particles (eBook)

Preface 6
Contents 7
1 Introduction 12
Part I Nonrelativistic Collisions 16
2 First Order Considerations 17
2.1 Quantum Plane-Wave Born Approximation 17
2.2 Semi-Classical Approach 22
3 Considerations Beyond First Order Perturbation Theory 26
3.1 Second Order Approximation 26
3.2 Distorted-Wave Approach 29
3.3 Coupled Channel Approach 37
3.4 Sudden Approximation 39
3.5 Glauber Approximation 42
3.6 Classical Trajectory Monte Carlo Approach 44
3.7 Projectile Electron Loss. Comparison with Experiment 46
Part II Relativistic Collisions 57
4 Introduction to Relativistic Collisions 58
4.1 Elements of the Special Theory of Relativity 58
4.2 The Electromagnetic Field 64
4.3 The Dirac Equation 67
5 Descriptions of Collisions Within the First Order Approximation in the Projectile – Target Interaction 73
5.1 Preliminary Remarks 73
5.2 Simpli.ed Semi-Classical Consideration 76
5.3 Plane-Wave Born Approximation 79
5.4 Semi-Classical Approximation 85
5.5 Relativistic Features and the Nonrelativistic Limit 89
5.6 Consideration on the Base of Quantum Electrodynamics 90
5.7 Gauge Independence and the Continuity Equation 92
5.8 Calculations in the Coulomb Gauge 94
5.9 Simpli.cation of the Atomic Transition Four- Current: The ‘ Nonrelativistic Atom’ Approximation 96
5.10 Manipulations with the Transition Matrix Elements as a Change of Gauge 102
5.11 Projectile-Electron Transitions as a Three- Body Problem 106
5.12 Relativistic Ion–Atom Collisions and Nonrelativistic Form- Factors 118
5.13 Electron–Positron Pair Production in Collisions of Bare Ions with Neutral Atoms 119
5.14 Two-Center Dielectronic Transitions 120
6 Theoretical Methods Extending beyond the First Order Approximation 136
6.1 Collisions with Light Atoms: Preliminary Remarks 136
6.2 Symmetric Eikonal Model 137
6.3 Collisions with Heavy Atoms: Preliminary Remarks 153
6.4 Extreme Relativistic Collisions with Heavy Atoms 154
6.5 Collisions at Relatively Low Energies: Three- Body Distorted- Wave Models 173
6.6 The High-Energy Limit of the Distorted- Wave Models 181
6.7 Nonperturbative Approaches 184
7 Impact Parameter Dependence of Projectile- Electron Excitation and Loss in Relativistic Collisions 192
7.1 Preliminary Remarks 192
7.2 Transition Amplitudes 193
7.3 Excitation of Bi82+(1s) in Collisions with Cu and He 196
7.4 Higher-Order E.ects in the Loss Probability in Collisions at Asymptotically Large . 201
8 Cross Sections and Comparison with Experiment 206
8.1 Electron Loss in Collisions at Low . 206
8.2 Excitation and Simultaneous Excitation-Loss in Collisions at Low . 211
8.3 Electron Loss in Collisions at Moderately High . 216
8.4 Collisions at High .: Electron Loss and Capture Cross Sections 220
8.5 Screening E.ects in Free–Free Pair Production 226
8.6 Charge States of 33TeV Pb Projectiles Penetrating Solid Targets: Multiple Collision E . ects 227
8.7 Di.erential Loss Cross Sections in Collisions at High . 234
8.8 On the Longitudinal and Transverse Contributions to the Total Loss Cross Section 244
8.9 Loss Cross Sections at Asymptotically High .: Saturation E . ect 246
8.10 Excitation and Break-Up of Pionium in Relativistic Collisions with Neutral Atoms 249
8.11 Higher-Order E.ects at Asymptotically High . 251
A Appendix 253
A.1 Nonrelativistic Atom Approximation for the Screening Mode 253
A.2 The Schr¨ odinger–Pauli Equation and Relativistic Collisions 254
A.3 On the Existence of the ‘Overlap’ Region 263
A.4 Radiative Atomic Processes and Galilean and Gauge Transformations 265
References 280