Nonrelativistic Quantum X-Ray Physics E-Book

Stefan P. Hau-Riege

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 357

Veröffentlichungsjahr: 2014

Beschreibung

Providing a solid theoretical background in photon-matter interaction, Nonrelativistic Quantum X-Ray Physics enables readers to understand experiments performed at XFEL-facilities and x-ray synchrotrons. As a result, after reading this book, scientists and students will be able to outline and perform calculations of some important x-ray-matter interaction processes. Key features of the contents are that the scope reaches beyond the dipole approximation when necessary and that it includes short-pulse interactions. To aid the reader in this transition, some relevant examples are discussed in detail, while non-relativistic quantum electrodynamics help readers to obtain an in-depth understanding of the formalisms and processes.
The text presupposes a basic (undergraduate-level) understanding of mechanics, electrodynamics, and quantum mechanics. However, more specialized concepts in these fields are introduced and the reader is directed to appropriate references. While primarily benefiting users of x-ray light-sources, the material is equally of relevance to researchers in various disciplines, such as life sciences, biology, materials science, physics, and chemistry that plan on applying these new facilities in their respective fields.

Leseprobe

Table of Contents

Cover

Related Titles

Title Page

Copyright

Dedication

Preface

Part I: Introduction

Chapter 1: Introduction

1.1 Motivation

1.2 Comparing X-Rays with Optical Radiation

1.3 Novel X-Ray Sources

1.4 Unit Systems

1.5 Overview of Lagrangian and Hamiltonian Mechanics

1.6 Approximations

Chapter 2: Review of Some Concepts in Quantum Mechanics

2.1 Introduction

2.2 Dirac's Bra–Ket (Bracket) Notation

2.3 Eigenvalues and Eigenfunctions

2.4 Functions of Operators

2.5 Point Particle in a Radially Symmetric Potential

2.6 Mixed States

2.7 Schrödinger and Heisenberg Pictures of Quantum Mechanics

2.8 Representing Quantum Mechanics in Position and Momentum Space

2.9 Transition from Classical Mechanics to Quantum Mechanics

2.10 Molecular Orbital Approximation

Part II: Quantization of the Free Electromagnetic Field

Chapter 3: Classical Electromagnetic Fields

3.1 Introduction

3.2 Maxwell's Equations

3.3 Electromagnetic Potentials

3.4 Transverse and Longitudinal Maxwell's Equations

3.5 The Free Electromagnetic Field as a Sum of Mode Oscillators

3.6 Charged Particle in an Electromagnetic Field and the Minimal-Coupling Hamiltonian

Chapter 4: Harmonic Oscillator

4.1 Introduction

4.2 Classical Harmonic Oscillator with One Degree of Freedom

4.3 Quantum Mechanical Harmonic Oscillator

4.4

N

-Dimensional Quantum Mechanical Harmonic Oscillator

Chapter 5: Quantization of the Electromagnetic Field

5.1 Introduction

5.2 Transition to a Quantum Mechanical Description

5.3 Photon Number States (hucFock States)

5.4 Photons

Chapter 6: Continuous Fock Space

6.1 Introduction

6.2 Three-Dimensional Continuum Field

6.3 One-Dimensional Treatment

Chapter 7: Coherence

7.1 Introdcution

7.2 Review of Classical Coherence Theory

7.3 Quantum Coherence Theory

Chapter 8: Examples for Electromagnetic States

8.1 Introduction

8.2 Quantum Phase of Radiation Fields

8.3 Single-Mode States

8.4 Multimode States

8.5 One-Dimensional Continuum Mode States

Part III: Interaction of X-Rays with Matter

Chapter 9: Interaction of the Electromagnetic Field with Matter

9.1 Introdution

9.2 Tensor Product of Matter and Radiation Hilbert Spaces

9.3 Interaction Hamiltonian for the Electromagnetic Field and Matter

Chapter 10: Time-Dependent Perturbation Theory

10.1 Introduction

10.2 Interaction Picture

10.3 Transition Probabilities

10.4 Perturbative Expansion of Transition Amplitudes

10.5 Time-Dependent Perturbation Theory for Mixed States

Chapter 11: Application of Perturbation Theory to the Interaction of Electromagnetic Fields with Matter

11.1 Introduction

11.2 Feynman Diagrams

11.3 Mixed States

Part IV: Applications of X-Ray-Matter-Interaction Theory

Chapter 12: X-Ray Scattering by Free Electrons

12.1 Introduction

12.2 Energy and Momentum Conservation

12.3 Scattering Cross Section

12.4 Scattering From an Electron at Rest

12.5 Doppler Effect

Chapter 13: Radiative Atomic Bound–Bound Transitions

13.1 Introduction

13.2 Emission of Photons

13.3 Lifetime and Natural Line Width

13.4 Absorption of Photons

13.5 Einstein's

A

and

B

Coefficients

13.6 Radiative Atomic Bound–Bound Transitions in Mixed States

Chapter 14: One-Photon Photoionization

14.1 Introduction

14.2 Photoionization in a Pure-State Radiation Field

14.3 Photoionization in a Mixed-State Radiation Field

14.4 Single-Electron Approximation for Photoionization

14.5 Photoionization of Hydrogen-Like Atoms

Chapter 15: Bremsstrahlung

15.1 Introduction

15.2 Electron–Nucleus Bremsstrahlung

15.3 Electron–Positron Bremsstrahlung

15.4 Electron–Electron Bremsstrahlung

15.5 Inverse Bremsstrahlung Absorption

Chapter 16: X-Ray Scattering

16.1 Introduction

16.2 Steady-State Scattering Formalism

16.3 Elastic Scattering (Rayleigh Scattering)

16.4 Raman Scattering

16.5 Compton Scattering

16.6 Single-Electron Approximation for X-Ray Scattering

16.7 Short-Pulse Scattering

Chapter 17: Relaxation Processes

17.1 Introduction

17.2 Auger Decay

17.3 X-Ray Fluorescence following Photoionization

17.4 Branching Ratio

Chapter 18: Multiphoton Photoionization

18.1 Introduction

18.2 Above-Threshold Ionization

18.3 Sequential Two-Photon Absorption

Chapter 19: Threshold Phenomena

19.1 Introduction

19.2 One-Step Treatment of Threshold Excitations

19.3 Nonradiative Threshold Processes

References

Index

End User License Agreement

Pages

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

59

60

61

62

63

64

65

67

68

69

70

71

72

73

74

75

77

78

79

80

81

82

83

84

85

86

87

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

127

128

129

130

131

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

221

222

223

224

225

226

227

228

229

230

231

232

233

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

277

278

279

280

281

282

283

285

286

287

288

289

290

291

1

41

125

165

Guide

Cover

Table of Contents

Preface

Part I: Introduction

Chapter 1: Introduction

List of Illustrations

Figure 1.1

Figure 3.1

Figure 3.2

Figure 7.1

Figure 8.1

Figure 9.1

Figure 10.1

Figure 10.2

Figure 10.3

Figure 11.1

Figure 11.2

Figure 12.1

Figure 12.2

Figure 12.3

Figure 12.4

Figure 12.5

Figure 12.6

Figure 12.7

Figure 12.8

Figure 13.1

Figure 14.1

Figure 14.2

Figure 14.3

Figure 14.4

Figure 14.5

Figure 14.6

Figure 14.7

Figure 15.1

Figure 15.2

Figure 15.3

Figure 16.1

Figure 16.2

Figure 16.3

Figure 16.4

Figure 16.5

Figure 16.6

Figure 17.1

Figure 17.2

Figure 17.3

Figure 17.4

List of Tables

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Table 2.1

Table 10.1

Table 15.1

Related Titles

Zettili, N.

Quantum Mechanics - Concepts and Applications 2e

Second Edition

2008

ISBN: 978-0-470-02679-3

Also available in digital formats.

He, B.B.

Two-dimensional X-ray Diffraction

2009

Print ISBN: 978-0-470-22722-0

Also available in digital formats.

Willmott, P.

An Introduction to Synchrotron Radiation - Techniques and Applications

2011

ISBN Softcover: 978-0-470-74578-6

ISBN Hardcover: 978-0-470-74579-3

Also available in digital formats.

Als-Nielsen, J., McMorrow, D.

Elements of Modern X-ray Physics 2e

Second Edition

2011

ISBN: 978-0-470-97394-3

Also available in digital formats.

Landau, R.H.

Quantum Mechanics II

A Second Course in Quantum Theory

Second Edition

1995

ISBN: 978-0-471-11608-0

Also available in digital formats.

Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.

Photons and Atoms

Introduction to Quantum Electrodynamics

1989

ISBN: 978-0-471-18433-1

Also available in digital formats.

Mandl, F., Shaw, G.

Quantum Field Theory 2e

Second Edition

2010

ISBN: 978-0-471-49684-7

Also available in digital formats.

Stefan P. Hau-Riege

Nonrelativistic Quantum X-Ray Physics

Author

Dr. Stefan P. Hau-Riege

Lawrence Livermore

National Laboratory

Livermore, CA, USA

[email protected]

Cover Design

The cover figure shows a stylized depiction of the atomic Compton scattering process.

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

© 2015 Wiley-VCH Verlag GmbH & Co. KGaA,

Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978-3-527-41160-3

ePDF ISBN: 978-3-527-66452-8

ePub ISBN: 978-3-527-66451-1

Mobi ISBN: 978-3-527-66450-4

oBook ISBN: 978-3-527-66449-8

For my parents

Preface

The increasing significance of photon sciences has manifested itself in the worldwide construction boom of new X-ray synchrotrons, including PETRA III at DESY in Germany and NSLS-II in the United States, and other novel high-intensity X-ray sources, such as X-ray free-electron lasers (XFELs). Following the pioneering work at the FLASH VUV free-electron laser (FEL) at DESY and at the linac coherent light source (LCLS) XFEL at SLAC National Accelerator Laboratory in the United States, a number of additional facilities have already or will soon become available, including the XFEL at SPring-8 Japan, the XFEL at DESY, the European UV/VUV FEL FERMI at Elettra in Italy, and the SwissFEL built by the Paul Scherrer Institute. Because of the remarkable photon output characteristics of these light sources with femtosecond pulse lengths, submicrometer focal sizes, and peak brightnesses that are up to times larger than previous-generation facilities, it is timely to revisit the basic theory of X-ray–matter interaction physics. Whereas a classical description of radiation fields has been very successful in the past, these novel X-ray sources require us to reconsider important pertinent questions, including the following: What are the limitations of a classical description? How does X-ray–matter interaction change for ultrashort pulses? Are single-photon processes still dominant or do multiphoton processes occur? How do X-ray processes change near atomic resonances?

These and related questions can be answered satisfactorily only within a quantum theory. This book gives a full quantum mechanical description of the interaction of X-rays with matter. This consistent and unified treatment focuses specifically on the states of light relevant for current and future XFELs, and how they affect X-ray–matter interaction processes. We describe (i) the quantization of the electromagnetic field, (ii) the fundamentals of the interaction of radiation with matter, and (iii) the most basic X-ray processes involving electrons, atoms, and molecules. These X-ray processes include photon scattering by electrons, radiative bound–bound transitions, one-photon photoionization, Bremsstrahlung emission and absorption, X-ray scattering by atoms, multiphoton absorption, nonlinear optical processes, and relaxation phenomena. For each process, we describe the general physics and the theoretical formalism, and in many cases apply it to simple model systems, for example, matter described by the independent particle approximation or hydrogen-like atoms. These examples rely heavily on the recent and in some cases on more or less ancient scientificliterature.

Similar books have been published for the optical wavelength regime, but we focus specifically on X-ray radiation. X-ray wavelengths are on the order of the interatomic distances, and the associated X-ray energies are comparable to the transition and ionization energies of atoms and ions. Therefore, the relevant physical processes and their theoretical description can be very different from the processes occurring at longer wavelengths. In the optical regime, the photon wavelength is typically much larger than atomic length scales characterized by the variable a. In this case, the mathematics and physics are significantly simplified because terms proportional to can be neglected. Such a dipole approximation is not necessarily valid for X-rays and needs to be reconsidered on a case-by-case basis. Whereas we tend to avoid the dipole approximation, we do limit ourselves to a nonrelativistic treatment, which is usually sufficient to describe experiments performed at current fourth-generation light sources with X-ray energies up to 10–30 keV. The advantage of this simplified description is that the mathematics is simpler and the physical concepts are easier to convey.

This book will require a basic undergraduate-level understanding of mechanics, electrodynamics, and quantum mechanics. Some of the more specialized concepts in these fields are introduced in the early chapters of the book, and the reader will be directed to appropriate references.

I would like to thank my wife Christine as well as Jamie and Justin for their patience and support.

Stefan P. Hau-Riege

Fremont

March 2014

Part IIntroduction

In the first part of this book, we give a general introduction and review all the aspects of classical electrodynamics and quantum mechanics that are needed in later chapters. This brief summary will help us also to agree on the notation used throughout. The reader may very well be familiar with most of the material presented here, in which case it could be skipped and referred back to if needed.

1Introduction

1.1 Motivation

X-ray physics has been essential throughout the last century and continues to be so to this date. It has catalyzed and survived multiple revolutions in physics, and has undergone several renaissances, usually coupled with the advent of new generations of X-ray sources. A couple of events are particularly noteworthy: In 1900, Planck provided an explanation for the spectrum that is emitted by a thermal radiation source by assuming that the radiation is quantized into energy packets of magnitude per mode [1, 2]. In 1905, Einstein explained the photoelectric effect by assuming that electromagnetic radiation is corpuscular [3]. It has been shown since that a semiclassical theory, which treats the electromagnetic radiation classically and only the matter system quantum mechanically, is actually sufficient to explain this effect. Nevertheless, both Planck's and Einstein's observations suggested that classical electromagnetic field theory needs to be extended to include corpuscular and nondeterministic elements. By combining the special theory of relativity with quantum physics, scientist such as Dirac [4], Feynman [5], Schwinger [6], and Tomonaga [7] developed quantum electrodynamics (QED), the quantum theory of light, which is one of the crown jewels of modern physics. In this book, we develop and apply QED in its nonrelativistic limit, as it is sufficient for many current X-ray applications.

1.2 Comparing X-Rays with Optical Radiation

For optical radiation, the invention of the laser [8], an acronym for light amplification by stimulated emission of radiation, led to experiments that could only be understood with a quantum theory of radiation. It thereby greatly accelerated the development of the field of quantum optics in the 1960s. We build on the achievements made in that discipline and describe their extension to the X-ray regime.

X-ray and optical radiation fields are very similar in principle, but there are striking differences for practical applications. For example, unlike for optical radiation, X-ray wavelengths are comparable to atomic dimensions and interatomic distances, so they offer the potential to analyze structures with atomic resolution when we use techniques such as elastic X-ray scattering. The photon energy E is related to the wavelength and the light frequency through

1.1

Here, h is the Planck constant, is the reduced Planck constant, and c is the speed of light. Figure 1.1 shows the spatial extent of atoms measured by the radial expectation value as a function of the atomic charge number and for different atomic shells. It can be seen that is of the same order of magnitude as typical X-ray wavelengths.

Figure 1.1 Ionization energies , shown as black lines and related to the bottom axis, and the radial expectation values , shown as grey lines related to the top axis, of neutral atoms as a function of the atomic charge number Z. The top and the bottom axes are aligned so that an energy at the bottom, interpreted as an X-ray energy, corresponds to the wavelength shown at the top.

In the X-ray regime, inner-shell atomic processes tend to dominate. Excited atomic states decay quickly and exhibit an element-specific response associated with the emission of electrons or photons that are characteristic for the participating atomic shells. Also shown in Figure 1.1 are the ionization energies for different principal shells, corresponding to X-ray absorption edges. Both analyzing the relaxation products and tuning the X-ray energy to an atomic resonance and thereby identifying the atoms can be used for the analysis of materials. The details of these resonances depend also on the atomic environment, making it a useful tool to study nearest neighbor interactions. The interaction of X-rays with matter is generally relatively weak, as long as we stay away from atomic resonant energies, so that materials tend to be relatively transparent to X-rays.

1.3 Novel X-Ray Sources

Advances in the development of X-ray sources, such as synchrotrons and, more recently, X-ray free-electron lasers (FELs), continue to excite interest in the X-ray science community. We now discuss the major devices and techniques used to produce X-rays at such facilities, which are mostly based on utilizing the synchrotron radiation emitted by relativistic electron bunches in a magnetic field. If the Lorentz factor , where is the kinetic energy of an electron and