Classical Treatment of Collisions Between Ions and Atoms or Molecules (Springer Series on Atomic, Optical, and Plasma Physics, 118)

Since the beginning of the twentieth century, many experimental and theoretical works have been devoted to collisions between highly charged ions and atomic and molecular targets. It was realized that quantum mechanics is the only way, a priori, to describe such atomic phenomena. However, since quantum mechanics is very difficult to apply for collision systems with more than two particles, classical methods were very soon introduced and applied to simple collision systems and, subsequently, to more complicated systems. The results obtained by such classical methods were found to be surprisingly good, and classical mechanics is now well established, despite its approximations, as a replacement for or competition with quantum mechanics in many cases. In this book, the author will focus on the development of classical methods for describing collisional and post-collisional processes. The results will be compared with those found using quantum mechanical models, in order to demonstrate the ability of the classical approach to obtain many features and details of collision systems. Preface Acknowledgments Contents 1 Classical Mechanics—Goal and First Results 1.1 The Goal of Classical Mechanics 1.2 First Contributions of Classical Mechanics in Atomic Processes 1.2.1 The Rutherford Model 1.2.2 The Bohr Model 1.2.3 Sommerfeld Model References 2 Classical Mechanics’ Approaches in Atomic Collisions 2.1 Binary Encounter Models 2.1.1 Brief Description of the Model and Results 2.1.2 Improvements of the BE Model 2.2 Classical Over-Barrier Model 2.2.1 Introduction 2.2.2 Principle of the Model for Single Electron Capture 2.2.3 Multi-Electron Capture 2.3 Classical Trajectory Monte Carlo Method 2.3.1 Origin of the Method and Preliminary Applications 2.3.2 Brief Description of CTMC Method 2.3.3 Equations of Motion and Preparation of the System 2.3.4 Spatial and Momentum Initial Distributions 2.3.5 Integration Method and Variable Time Step 2.4 Interaction Potentials 2.4.1 Coulombic Potentials 2.4.2 Effective Coulombic Potentials 2.4.3 Inclusion of Electron Correlation 2.5 Collision and Post-Collision Processes 2.5.1 Collision Processes 2.5.2 Post-Collision Processes 2.5.3 Processes Selection Criteria in Classical Mechanics 2.6 Total, Partial and Differential Cross Sections 2.6.1 Total Cross Sections 2.6.2 Partial Cross Sections 2.6.3 Differential Cross Sections References 3 Classical Treatment of Aq+ + H Collisions 3.1 Interest and Motivation 3.2 H+ + H Collisions 3.2.1 Total Cross Sections 3.2.2 Partial Cross Sections 3.2.3 Differential Cross Sections 3.3 Aq+ (q > 1) + H Collisions 3.3.1 Total Cross Sections 3.3.2 Differential Cross Sections 3.4 The Role of Interferences in Collisions 3.4.1 Description of Interferences in Classical Mechanics 3.4.2 Interferences in H+ + H Collisions 3.4.3 Interferences in He2+ + H Collisions References 4 Classical Treatment of Aq+ + He Collisions 4.1 Interest and Motivation 4.2 Processes in Aq+ + He Collisions 4.3 Total and Partial Cross Sections 4.3.1 Total Cross Sections 4.3.2 Partial Cross Sections 4.4 Single and Multiple Differential Cross Sections 4.4.1 Single Differential Cross Sections 4.4.2 Multiple Differential Cross Sections 4.5 Extension of the CTMC Model to Specific Problems 4.5.1 Autoionization Following Double Electron Capture at Low Velocities 4.5.2 Single Ionization at High Velocities—Perpendicular Momentum Distributions 4.5.3 Extension to Fully Differential Cross Sections 4.6 Preliminary Conclusion References 5 Extension of CTMC Calculations to Multielectron Systems 5.1 Interest and Motivation 5.2 Simple Models for a Preliminary Study 5.2.1 Classical Over Barrier Model 5.2.2 Scaling Law for Multiple Electron Capture 5.3 CTMC Calculations 5.3.1 Collisions Involving Alkali-Metal Series 5.3.2 Collisions with Noble Targets 5.3.3 Combination of Processes References 6 Collisions Aq+ + H2 6.1 Goal of the Present Study 6.2 Collisions Involving H2+ Ions 6.2.1 H + H2+ Collisions 6.2.2 H + H2+ Collisions 6.3 Collisions Involving H2 Molecular Targets 6.3.1 Total and Partial Cross Sections 6.3.2 The Role of Electron Correlation 6.3.3 Differential Cross Sections 6.3.4 Molecular Target Fragmentation References 7 Collisions of Aq+ and Multielectron Molecular Targets 7.1 Interest of the Study 7.1.1 Molecules in Coma 7.1.2 Molecular Interaction in Cells 7.2 Collisions Involving H2O Targets 7.2.1 The Different Models 7.2.2 Total and Partial Cross Sections 7.2.3 Multiple Electron Processes 7.2.4 Differential Cross Sections 7.2.5 Fragmentation of the H2O Molecule 7.2.6 Introduction of Quantum Effects 7.3 Collisions Involving Biological Molecules 7.4 Track Structure Simulations 7.4.1 Principle of the Method 7.4.2 A Few Results References 8 Conclusions and Perspectives 8.1 Conclusions 8.2 Perspectives 8.2.1 H+ + H Collisions 8.2.2 Ne10+ + He Auger Effect Dependence onto the Projectile Energy 8.3 Classical Description of the H2 Molecule Including Electron Correlation 8.4 Double Capture Following He2+ + H2 Capture References Appendix A Extensions of the Classical Over-Barrier Model A.1 Charge Exchange Model for Atoms A.1.1 Motivation A.1.2 Description of the Model A.1.3 Applications A.1.3.1 O8+ + H Collisions A.1.3.2 Aq+ + Cs(6s) Collisions A.2 Angular Momentum Distributions of Electron Capture A.2.1 Goal of the Model A.2.2 Determination of Angular Momentum Distributions Appendix B Classical Radial and Momentum Distributions B.1 Continuous Distributions with Variable Energies B.1.1 Wigner Distributions B.1.2 Cohen and Sattin Distributions B.2 Quasi-Continuous Radial Distributions with Discrete Energies B.3 Quasi-Continuous Radial Distributions with Discrete Charges Appendix C Evolution of Integration Precision with Variable Time Step C.1 Two-Body Problem: C6+ + He2+ Collision C.2 Three-Body Problem: C6+ + He Collision Index