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E-raamat: Particle Penetration and Radiation Effects Volume 2: Penetration of Atomic and Molecular Ions

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This book represents volume 2 of a 3-volume monograph on Particle Penetration and Radiation Effects. While volume 1 addressed the basic theory of scattering and stopping of swift point charges, i.e., protons, antiprotons and alpha particles, the present volume focuses on ions heavier than helium as well as molecules and clusters over an energy range from a few keV/u to a few hundred MeV/u. The book addresses the foundations in atomic-collision physics of a wide variety of application areas within materials and surface science and engineering, micro and nano science and technology, radiation medicine and biology as well as nuclear and particle physics. Problems have been added to all chapters. This should make the book useful for both self-study and advanced university courses. An effort has been made to establish a unified notation throughout the monograph.

From the contents: Part I Charge States of Swift Ions.- Charge Equilibrium.- Charge Exchange: Atomistics.- Charge Exchange: Statistics and Energetics.- Part II Energy Loss of Swift Ions.- Stopping.- Straggling.- Part III Scattering.- Interatomic Potentials, Scattering and Nuclear Stopping.- Multiple Scattering.- Part IV Slow Ions.- Stopping of Slow Ions.- Range and Energy Deposition.- Part V Penetration of Aggregates.- Penetration of Molecules and Clusters.- Part VI Penetration Through Crystals.- Channeling and Blocking of Energetic Particles in Crystals.
General Notations xxiii
Part I Charge States of Swift Ions
1 Charge Equilibrium
3(42)
1.1 Introductory Comments
3(2)
1.2 Qualitative Orientation
5(1)
1.3 Stripping Criteria
6(5)
1.3.1 Velocity Criterion
6(3)
1.3.2 Energy Criterion
9(2)
1.4 Thomas-Fermi Theory
11(11)
1.4.1 Thomas-Fermi Equation for an Atomic Ion
11(2)
1.4.2 Solution
13(3)
1.4.3 Trial Function Approach
16(2)
1.4.4 Examples of Trial Functions
18(2)
1.4.5 Brandt-Kitagawa Theory
20(2)
1.5 Effect of the Stopping Medium
22(6)
1.5.1 Linear Theory
22(3)
1.5.2 Application to Light Ions
25(1)
1.5.3 Wake-Riding Electrons
26(1)
1.5.4 Effect of Screening
27(1)
1.6 Data
28(5)
1.6.1 Pas-Solid Difference
29(1)
1.6.2 Compilations
29(4)
1.7 Discussion and Outlook
33(1)
1.8 Appendix
34(5)
1.8.1 Exchange Energy in the Thomas-Fermi Equation
34(2)
1.8.2 Thomas-Fermi-Dirac Theory
36(3)
Problems
39(1)
References
39(6)
2 Charge Exchange: Atomistics
45(52)
2.1 Introductory Comments
45(1)
2.2 Charge-Changing Events
46(2)
2.3 Early Estimates
48(3)
2.3.1 Double Scattering: The Thomas Process
48(2)
2.3.2 Bohr's Model
50(1)
2.4 Quantum Theory of One-Electron Capture
51(21)
2.4.1 A Qualitative Estimate
51(2)
2.4.2 General Considerations
53(1)
2.4.3 Semiclassical Theory
53(4)
2.4.4 First-Order Perturbation
57(8)
2.4.5 Beyond First-Order Perturbation Theory
65(7)
2.5 Multiple-Electron Systems
72(5)
2.5.1 Classical Models
72(4)
2.5.2 Data
76(1)
2.6 Radiative Electron Capture
77(8)
2.6.1 Detailed Balance
79(2)
2.6.2 Photoemission
81(3)
2.6.3 Examples
84(1)
2.7 Electron Loss
85(4)
2.7.1 Single and Multiple Loss
86(1)
2.7.2 Theoretical Schemes
87(2)
2.7.3 Data
89(1)
2.8 Discussion and Outlook
89(1)
Problems
90(1)
References
91(6)
3 Charge Exchange: Statistics and Energetics
97(52)
3.1 Introductory Comments
97(1)
3.2 Statistics of Charge and Excitation States
98(8)
3.2.1 Transition Matrix
98(2)
3.2.2 Rate Equations
100(1)
3.2.3 Spontaneous Processes
101(1)
3.2.4 Examples
101(5)
3.2.5 Eigenvalue Expansion
106(1)
3.3 Charge Equilibrium
106(9)
3.3.1 Continuum Approximation
107(2)
3.3.2 Gaussian Apparoximation
109(1)
3.3.3 Gas-Solid Difference
110(5)
3.4 Energetics of Charge Exchange
115(8)
3.4.1 Definitions
115(1)
3.4.2 Electron Capture: One Dimension
116(1)
3.4.3 Planar Collision: Excitation only
117(2)
3.4.4 Planar Collision: Electron Capture
119(1)
3.4.5 Three-dimensional Collision: Electron Loss
119(1)
3.4.6 Elastic and Inelastic Energy Loss
120(2)
3.4.7 Radiative Electron Capture
122(1)
3.4.8 Spontaneous Processes
122(1)
3.5 Statistics of Energy Loss and Charge Exchange
123(18)
3.5.1 Generalized Bothe-Landau Formula
123(2)
3.5.2 Transport Equations
125(1)
3.5.3 Mean Energy Loss
125(4)
3.5.4 State-Specific Mean Energy Loss
129(4)
3.5.5 Straggling
133(5)
3.5.6 Energy-Loss Profiles
138(3)
3.6 Discussion and Outlook
141(1)
Problems
142(1)
References
143(6)
Part II Energy Loss of Swift Ions
4 Stopping
149(48)
4.1 Introductory Comments
149(2)
4.2 Experiments
151(1)
4.3 Effective Charge and its Problems
152(4)
4.4 Bohr Theory Extended
156(2)
4.4.1 Low-Speed Limit
156(1)
4.4.2 Screening
156(2)
4.4.3 Charge Dependence
158(1)
4.5 Binary Stopping Theory and PASS Code
158(8)
4.5.1 The Kernel
159(2)
4.5.2 Multiple-Electron Atoms
161(2)
4.5.3 Projectile Excitation and Ionization
163(2)
4.5.4 Extension into the Bethe Regime
165(1)
4.5.5 Shell Correction
165(1)
4.5.6 Relativistic Effects
166(1)
4.6 PCA/UCA Approximation and CasP Code
166(3)
4.6.1 The Kernel
167(1)
4.6.2 Extensions
168(1)
4.7 Transport Cross Section
169(5)
4.7.1 A General Remark
170(1)
4.7.2 Generalized Friedel Sum Rule
171(2)
4.7.3 Convergent Kinetic Theory (CKT)
173(1)
4.8 Applications
174(9)
4.8.1 Equilibrium Stopping Forces from PASS and CasP
174(3)
4.8.2 Equilibrium Stopping Forces from Empirical Tabulations
177(1)
4.8.3 Charge-Dependent Stopping
178(4)
4.8.4 Stopping in Compound Materials
182(1)
4.9 Impact-Parameter-Dependent Energy Loss
183(5)
4.9.1 Local-Density Approximation
184(1)
4.9.2 Born Approximation
185(1)
4.9.3 PCA/UCA Approximation
185(1)
4.9.4 Binary Theory
185(2)
4.9.5 Examples
187(1)
4.10 Discussion and Outlook
188(2)
Problems
190(1)
References
190(7)
5 Straggling
197(38)
5.1 Introductory Comments
197(1)
5.2 General Considerations
198(3)
5.2.1 Validity of the Gaussian Approximation
200(1)
5.2.2 Correlated and Uncorrelated Straggling
200(1)
5.3 Uncorrelated Straggling
201(6)
5.3.1 Screening
202(2)
5.3.2 Transition to the Bethe regime
204(1)
5.3.3 Shell and Barkas-Andersen correction
204(1)
5.3.4 Projectile Excitation and Ionization
205(1)
5.3.5 Relativity
206(1)
5.3.6 Electron Capture
207(1)
5.3.7 Short Summary of Linear Straggling
207(1)
5.4 Bunching and Packing
207(11)
5.4.1 Statistics
208(2)
5.4.2 Bunching: Atoms
210(2)
5.4.3 Packing: Molecules
212(2)
5.4.4 Packing: Solids
214(4)
5.5 Charge-Exchange Straggling
218(3)
5.5.1 Neglecting Energy Loss by Charge Exchange?
218(1)
5.5.2 Examples
219(2)
5.6 Dielectric Theory
221(4)
5.6.1 Recapitulation
221(2)
5.6.2 Local-Density Approximation
223(1)
5.6.3 Empirical Extension to Heavier Ions
223(2)
5.7 Data
225(1)
5.8 Discussion and Outlook
226(3)
Problems
229(1)
References
229(6)
Part III Scattering
6 Interatomic Potentials, Scattering and Nuclear Stopping
235(46)
6.1 Introductory Comments
235(1)
6.2 Potentials
236(14)
6.2.1 Bohr's Estimate
237(3)
6.2.2 Thomas-Fermi Theory
240(5)
6.2.3 Other Binary Potentials
245(4)
6.2.4 Nonbinary Potentials
249(1)
6.2.5 Power Potentials
250(1)
6.3 Screened-Coulomb Scattering
250(17)
6.3.1 Limitations of Classical Elastic-Scattering Theory
251(3)
6.3.2 Recapitulation
254(1)
6.3.3 Lindhard-Scharff Scaling
255(3)
6.3.4 Comparison of Differential Cross Sections
258(1)
6.3.5 Inversion
259(2)
6.3.6 Scattering Experiments
261(5)
6.3.7 Shadow Cone
266(1)
6.4 Nuclear Stopping
267(7)
6.4.1 Scaling Properties
268(1)
6.4.2 Power Cross Section
269(2)
6.4.3 Straggling
271(1)
6.4.4 Measurements of Nuclear Stopping
272(2)
6.5 Discussion and Outlook
274(1)
Problems
275(1)
References
276(5)
7 Multiple Scattering
281(62)
7.1 Introductory Comments
281(1)
7.2 Needs
282(1)
7.3 Statistics: Angular Distributions
283(13)
7.3.1 Two-Layer Argument
284(1)
7.3.2 Expansion in Legendre Polynomials
284(3)
7.3.3 Small-Angle Approximation
287(1)
7.3.4 Bothe Formula
288(1)
7.3.5 Collision Counting
289(3)
7.3.6 Excursion into Truncated Cross Sections
292(1)
7.3.7 Transport Equation
293(1)
7.3.8 Projected Distribution
294(1)
7.3.9 Packing
294(2)
7.4 Statistics: Correlated Distributions
296(3)
7.4.1 Lateral-Angular Distribution
296(1)
7.4.2 Energy-Angular Distribution
297(2)
7.4.3 Effect of Charge Exchange
299(1)
7.5 Approaches
299(7)
7.5.1 Moments and Cumulants
299(1)
7.5.2 Diffusion Limit
300(2)
7.5.3 An Integrable Example
302(1)
7.5.4 Transition to Single Scattering
303(1)
7.5.5 Bohr-Williams Model
304(2)
7.5.6 Simulation
306(1)
7.6 Angular Distribution
306(12)
7.6.1 Scaling properties
306(3)
7.6.2 Relativity
309(1)
7.6.3 Weak Screening
309(3)
7.6.4 Numerical Results
312(3)
7.6.5 Measurements
315(1)
7.6.6 Special Aspects
316(2)
7.7 Lateral Distribution
318(7)
7.7.1 Scaling Properties
318(2)
7.7.2 Power Scattering
320(1)
7.7.3 Numerical Results
321(1)
7.7.4 Measurements
321(2)
7.7.5 Packing
323(2)
7.7.6 Angular-Lateral Distribution
325(1)
7.8 Energy-Angular Distribution
325(9)
7.8.1 Separation of Nuclear from Electronic Stopping
327(2)
7.8.2 Angular Scan
329(3)
7.8.3 Trajectory Inversion
332(2)
7.9 Discussion and Outlook
334(1)
Problems
334(1)
References
335(8)
Part IV Slow Ions
8 Stopping of Slow Ions
343(74)
8.1 Introductory Comments
343(1)
8.2 Velocity-proportional Stopping?
344(6)
8.2.1 Stokes' Law
345(1)
8.2.2 Z1 Structure
346(1)
8.2.3 Reciprocity
346(3)
8.2.4 Threshold Behaviour
349(1)
8.3 Experimental Aspects
350(9)
8.3.1 Problems and Tools
350(2)
8.3.2 Data
352(6)
8.3.3 Stopping in Crystals
358(1)
8.4 Limitations to Additivity
359(3)
8.4.1 Conservation Laws in Inelastic Collisions
360(1)
8.4.2 Mean Energy Loss
361(1)
8.5 Free Target Electrons
362(16)
8.5.1 Lindhard Theory
362(3)
8.5.2 Transport Cross Section
365(1)
8.5.3 Fermi Gas
366(1)
8.5.4 Born Approximation
366(1)
8.5.5 Screening
367(1)
8.5.6 Partial Waves
368(5)
8.5.7 Local-Density Approximation
373(4)
8.5.8 Lindhard-Scharff Formula
377(1)
8.6 Bound Target Electrons
378(10)
8.6.1 Electron Promotion
379(1)
8.6.2 Firsov Theory
379(2)
8.6.3 Dependence on Atomic Radius
381(1)
8.6.4 Modifications
382(1)
8.6.5 Numerical Procedures
383(5)
8.7 Transition to Higher Energies
388(2)
8.8 Straggling
390(11)
8.8.1 General Considerations
390(2)
8.8.2 Free Target Electrons
392(6)
8.8.3 Bound Target Electrons
398(2)
8.8.4 Comparison with Experiment
400(1)
8.9 Discussion and Outlook
401(2)
8.10 Appendix
403(5)
8.10.1 The WKB Method
403(2)
8.10.2 Friedel Sum Rule
405(2)
8.10.3 Density Functional Theory
407(1)
Problems
408(1)
References
409(8)
9 Range and Energy Deposition
417(64)
9.1 Introductory Comments
417(3)
9.1.1 Recapitulation
418(2)
9.1.2 Needs
420(1)
9.2 Pathlength
420(10)
9.2.1 Integral Equation
421(1)
9.2.2 Moments
422(1)
9.2.3 Simple Solutions
423(1)
9.2.4 Profiles
424(1)
9.2.5 Input
425(1)
9.2.6 Scaling Properties
425(3)
9.2.7 Power Cross Section
428(2)
9.3 Projected and Lateral Range
430(14)
9.3.1 Integral Equation
430(1)
9.3.2 Range Parameters
431(1)
9.3.3 Input
432(2)
9.3.4 Mean Range
434(2)
9.3.5 Higher Moments
436(5)
9.3.6 Charge Exchange
441(3)
9.4 Deposited Energy
444(11)
9.4.1 Nuclear and Electronic Processes
445(1)
9.4.2 Zero-Order Moments
445(7)
9.4.3 Higher Moments
452(3)
9.5 Range and Energy-Deposition Profiles
455(14)
9.5.1 Construction from Moments
455(4)
9.5.2 Direct Methods
459(2)
9.5.3 Simulation Codes
461(2)
9.5.4 Measurements
463(6)
9.6 Fluctuations and Correlations
469(2)
9.7 Discussion and Outlook
471(1)
Problems
472(1)
References
473(8)
Part V Penetration of Aggregates
10 Penetration of Molecules and Clusters
481(68)
10.1 Introductory Comments
481(1)
10.2 Coulomb Explosion
482(5)
10.2.1 Dynamics
482(2)
10.2.2 Time Constant
484(1)
10.2.3 Transformation to the Laboratory Frame
484(2)
10.2.4 Energy and Angular Spectra
486(1)
10.3 Multiple Scattering
487(4)
10.3.1 Independent Atoms
487(1)
10.3.2 Correlated Scattering
488(1)
10.3.3 Examples
489(2)
10.4 Energy Loss
491(20)
10.4.1 Qualitative Considerations
492(1)
10.4.2 Born Approximation
493(6)
10.4.3 Classical Theory
499(4)
10.4.4 Dielectric Theory
503(6)
10.4.5 Large Clusters
509(2)
10.5 Charge State
511(7)
10.5.1 Observations
511(1)
10.5.2 Qualitative Considerations
512(1)
10.5.3 Estimates
513(5)
10.6 Correlations
518(10)
10.6.1 Ring Patterns
519(1)
10.6.2 Coulomb Explosion and Multiple Scattering
519(4)
10.6.3 Coulomb Explosion and Energy Loss
523(2)
10.6.4 Wake Effects
525(3)
10.7 Applications
528(2)
10.7.1 Energy Deposition
528(1)
10.7.2 Cotlomb Imaging
529(1)
10.8 Discussion and Outlook
530(1)
10.9 Appendix: Polarization Wake
530(9)
10.9.1 Point Charge
530(8)
10.9.2 Screened Ions
538(1)
Problems
539(2)
References
541(8)
Part VI Penetration through Crystals
11 Channeling and Blocking of Energetic Particles in Crystals
549(40)
11.1 Introduction
550(2)
11.2 Collision with String of Atoms
552(5)
11.2.1 Continuum Model
553(1)
11.2.2 Screened Potential
553(2)
11.2.3 Lindhard's Critical Angle
555(1)
11.2.4 Thermal Vibrations
556(1)
11.2.5 Dip in Yield
557(1)
11.3 Planar Channeling
557(1)
11.4 Channeling of Electrons and Positrons
558(3)
11.5 Channeling Radiation
561(3)
11.6 Dechanneling
564(1)
11.7 Applications
565(7)
11.7.1 Dechanneling by Crystal Defects
565(2)
11.7.2 Localization of Impurities by Channeling and Blocking
567(3)
11.7.3 Crystal Blocking for Determination of Nuclear Lifetimes
570(2)
11.8 Restricted Equilibrium in Axial Channeling
572(3)
11.9 Cooling and Heating in Ion Transmission through Crystals
575(4)
11.10 Secondary Processes
579(5)
11.10.1 Energy Loss for Channeled Particles
579(4)
11.10.2 Crystal as Special Target for Atomic Processes
583(1)
11.11 Concluding Remarks
584(1)
References
585(4)
Author and Subject Index 589