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X-Rays, Neutrons and Muons

ISBN: 978-3-527-30774-6
248 pages
September 2012
X-Rays, Neutrons and Muons (3527307745) cover image
Spectroscopy is a versatile tool for the characterization of materials, and photons in the visible frequency range of the electromagnetic spectrum have been used successfully for more than a century now. But other elementary particles such as neutrons, muons and x-ray photons have been proven to be useful probes as well and are routinely generated in modern cyclotrons and synchrotrons. They offer attractive
alternative ways of probing condensed matter in order to better understand its properties and to correlate material behavior with its structure. In particular, the combination of these different spectroscopic probes yields rich information on the material samples, thereby allowing for a systematic investigation down to atomic resolutions.

This book gives a practical account of how well they complement each other for 21st century material characterization, and provides the basis for a detailed understanding of the scattering processes and the knowledge of the relevant microscopic interactions necessary for the correct interpretation of the experimentally obtained spectroscopic data.
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Foreword V

Preface XI

About the Book XIII

1 Introduction 1

1.1 Some Historical Remarks 1

1.2 The Experimental Methods 2

1.3 The Solid as a Many Body 6

1.4 Survey over the Spectral Region of a Solid 9

References 11

2 The Probes, their Origin and Properties 13

2.1 Origin 13

2.1.1 The Photon 13

2.2 Properties 15

2.3 Magnetic Field of the Probing Particles 25

3 Interaction of the Probes with the Constituents of Matter 27

3.1 The Nuclear Interaction of Neutrons 27

3.2 Interaction of X-Rays with Atomic Constituents 36

3.3 Magnetic Interaction 49

3.4 Corollar 55

References 58

4 Scattering on (Bulk-)Samples 59

4.1 Introduction 59

4.2 The Sample as a Thermodynamic System 59

4.3 The Scattering Experiment 66

4.4 Properties of the Scattering and Correlation Function 83

4.5 General Form of Spin-Dependent Cross-Sections 88

4.6 Summary and Conclusions 123

References 125

5 General Theoretical Framework 127

5.1 Time Development of the Density Operator 127

5.2 Generalized Suspectibility 142

5.3 Dielectric Response Function and Sum Rules 157

References 173

Appendix A: Principles of Scattering Theory 175

A.1 Potential Scattering (Supporting Section 3.1.1) 175

A.2 Two Particle Scattering (Supporting Section 3.1.2) 179

A.3 Abstract Scattering Theory (Supporting Section 3.2) 180

A.4 Time-Dependent Perturbation 183

A.5 Scattering of Light on Atoms 186

A.6 Polarization and its Analysis 188

References 190

Appendix B: Form Factors 191

References 195

Appendix C: Reminder on Statistical Mechanics 197

C.1 The Statistical Operator P 197

C.2 The Equation of Motion 198

C.3 Entropy 198

C.4 Thermal Equilibrium – The Canonical Distribution 199

C.5 Thermodynamics 200

Appendix D: The Magnetic Matrix-Elements 203

D.1 The Trammell Expansion 203

D.2 The Matrix Elements 205

D.3 Conclusion 210

References 211

Appendix E: The Principle of a mSR-Experiment 213

Appendix F: Reflection Symmetry and Time-Reversal Invariance 217

F.1 Invariance Under Space Inversion Q 217

F.2 Invariance Under Time Reversal 218

Appendix G: Phonon Coupling to Heat Bath 221

References 223

Further Reading 225

Index 227

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Walter E. Fischer (1939-2008) was the former head of the Department of Condensed Matter Research with Neutrons and Muons (NUM) at the Paul Scherrer Institute (PSI) in Villigen, Switzerland. He pioneered in establishing the spallation neutron source SINQ at PSI which went into operation in the mid-1990s. Later he foundes a condensed matter theory group to complement the experimental work at the neutron source.
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