Quantum Theory of High-Energy Ion-Atom Collisions / Edition 1

by Dzevad Belkic

Overview

One of the Top Selling Physics Books according to YBP Library Services

Suitable for graduate students, experienced researchers, and experts, this book provides a state-of-the-art review of the non-relativistic theory of high-energy ion-atom collisions. Special attention is paid to four-body interactive dynamics through the most important theoretical methods available to date by critically analyzing their foundation and practical usefulness relative to virtually all the relevant experimental data.

Fast ion-atom collisions are of paramount importance in many high-priority branches of science and technology, including accelerator-based physics, the search for new sources of energy, controlled thermonuclear fusion, plasma research, the earth’s environment, space research, particle transport physics, therapy of cancer patients by heavy ions, and more.

These interdisciplinary fields are in need of knowledge about many cross sections and collisional rates for the analyzed fast ion-atom collisions, such as single ionization, excitation, charge exchange, and various combinations thereof. These include two-electron transitions, such as double ionization, excitation, or capture, as well as simultaneous electron transfer and ionization or excitation and the like—all of which are analyzed in depth in this book.

Quantum Theory of High-Energy Ion-Atom Collisions focuses on multifaceted mechanisms of collisional phenomena with heavy ions and atoms at non-relativistic high energies.

Product Details

ISBN-13:	9780367386450
Publisher:	Taylor & Francis
Publication date:	09/05/2019
Pages:	432
Product dimensions:	6.12(w) x 9.19(h) x (d)

Table of Contents

About the Author v

Preface vi

Acknowledgments viii

1 Basic notions and main observables in scattering problems 1

1.1 Observables and elementary processes 1

1.2 Energy as the most important physical property 2

1.3 Classification of collisions 5

1.4 The role of wave packets 8

1.5 Adiabatic switching of interaction potentials 9

1.6 Collimation of beams of projectiles 9

1.7 General waves and quantum mechanical waves 12

1.8 Probability character of quantum collisions 14

2 Requirements of the theory for the experiment 17

2.1 Elementary events versus multiple scatterings 22

2.2 Average probabilities 23

2.3 Total cross sections 24

2.4 Differential cross sections 30

2.5 Total probabilities 32

2.6 Transmission phenomena 33

2.7 Quantum mechanical currents and cross sections 36

3 Continuous spectrum and eigen-problems of resolvents 39

3.1 Completeness and separability of the Hilbert spaces 39

3.2 The key realizations of abstract vector spaces 41

3.3 Isomorphism of vector spaces 42

3.4 Eigen-problems for continuous spectra 45

3.5 Normal and Hermitean operators 51

3.6 Strong and weak topology 53

3.7 Compact operators for mapping of the weak to strong limits 58

3.8 Strong differentiability and strong analyticity 59

4 Linear and bilinear functionals 61

4.1 Linear functionals for mapping between vector spaces and scalar fields 61

4.2 The Ries-Freshe theorem 63

4.3 Bilinear functionals 66

5 Definition of a quantum scattering event 71

5.1 Hamiltonian operators and boundedness 71

5.2 Evolution operators and the Møller wave operators 72

5.3 The Cauchy strong limit in non-stationary scattering theory 73

5.4 Three criteria for a quantum collisional system 74

6 The adiabatic theorem and the Abel strong limit 79

6.1 Adiabatic theorem for scattering states 79

6.2 Adiabatic theorem and existence of wave operators 80

6.3 The Abel strong limit in stationary scattering theory 81

6.4 Exponential screening of potentials and adiabatic theorem 83

6.5 Adiabatic theorem and the Green operators 84

6.6 Adiabatic theorem and the Lippmann-Schwinger equations 85

7 Non-stationary and stationary scattering via the strong limits 87

7.1 The Abel limit and Lippmann-Schwinger equations 87

7.2 The Abel limit and Fourier integrals 95

8 Scattering matrix and transition matrix 97

8.1 The Abel limit and scattering operators 97

8.2 Matrix elements of scattering operators 99

8.3 Transition operators 101

9 Spectral analysis of operators 105

9.1 The Abel limit with no recourse to the Cauchy limit 105

9.2 The spectral theorem 106

9.3 Unitary operators and strong topology 108

9.4 The Abel limit for the Møiler wave operators 114

9.5 The link between the Møller operators and Green resolvents 120

10 The existence and completeness of the Møller wave operators 125

10.1 Linearity and isometry of wave operators 125

10.2 Boundedness of wave operators in the whole Hilbert space 126

10.3 The Schur lemma on invariant sub-spaces for evolution operators 126

10.4 Intertwining relations for evolution operators and wave operators 128

10.5 The role of spectral projection operators 130

10.6 Completeness of the Møller wave operators 133

10.7 Scattering operator derived from intertwining wave operators 135

11 Four-body theories for fast ion-atom collisions 139

11.1 Main features of interactive four-body dynamics 140

11.2 Notation and basic formulae 146

11.3 The entrance channel 147

11.3.1 The Z_P - (Z_T; e₁, e₂)i collisional system 147

11.3.2 The (Z_P, e₁)_iP - (Z_T, e₂)_i2 collisional system 150

11.4 The exit channels 151

11.4.1 Double electron capture 151

11.4.2 Single electron capture 154

11.4.3 Transfer ionization 156

12 Perturbation series with the correct boundary conditions 157

12.1 The Lippmann-Schwinger equations 158

12.2 The Born exepansions with the correct boundary conditions for four-body collisions 160

13 The Dodd-Greider series for four-body collisions 163

13.1 Derivation of the distorted waves for the initial states 167

13.1.1 The Z_P - (Z_T; e₁, e₂)_i collisional system 167

13.1.2 The (Z_P, e₁)_i1 - (Z_T, e₂)_i2 collisional system 170

14 Double electron capture 171

14.1 The CDW-4B method 171

14.2 The SE-4B method 174

14.3 The CDW-EIS-4B method 176

14.4 The CDW-EFS-4B method 177

14.5 The BDW-4B method 179

14.6 The BCIS-4B method 185

14.7 The CB1-4B method 188

14.8 Comparison between theories and experiments 190

14.8.1 Double electron capture into the ground state 190

14.8.2 Double electron capture into excited states 205

15 Simultaneous transfer and ionization 215

15.1 The CDW-4B method 215

15.2 Comparison between theories and experiments 220

16 Single electron detachment 231

16.1 The MCB-4B method 235

16.2 Comparison between theories and experiments 242

17 Single electron capture 259

17.1 The CDW-4B method 259

17.1.1 Differential cross sections: The Thomas double scattering at all energies 263

17.1.2 Total cross sections 265

17.2 The CDW-BFS (prior BDW-4B) and CDW-BIS (post BDW-4B method) 278

18 Electron capture by hydrogen-like projectiles 297

18.1 The CB1-4B method 297

18.2 Comparison between theories and experiments 301

19 Simultaneous Transfer and Excitation 313

19.1 The CDW-4B method for the TE process 314

19.2 The TEX mode for radiative decays of asymmetric systems 315

19.2.1 A model for the RTEX modes 315

19.2.2 A model for the NTEX modes 319

19.3 The CDW-4B method for the TEX modes 320

19.4 The CDW-4B method for the TE process in asymmetric collisions 321

19.4.1 The Kα - Kα emission line from S¹⁴⁺ 322

19.4.2 The Kα - Kβ emission lines from S¹⁴⁺ 325

19.5 Target charge Z_T and the interference between the RTEX and NTEX modes 326

19.6 The TEA mode for nearly symmetrical systems: the Auger decay 329

19.7 The CDW-4B method for the TEA modes 332

19.8 Description of the final state 333

19.9 Cross sections for the TEA modes 335

19.10 The CDW-4B method in the Feshbach resonance formalism 336

19.11 Comparison between theories and experiments for electron spectra near Auger peaks 337

19.11.1 Electron energy spectral lines 337

19.11.2 Total cross section for the TEA mode 343

20 Concluding remarks and outlooks 351

List of acronyms in the main text and bibliography 368

References 371

Index 407