This book arose from some lectures given in Cambridge in 1973 at a
Summer School organized by the Neutron Scattering Group of the
Institute of Physics and the Faraday Society. It is intended for experi-
menters in the field of thermal neutron scattering who wish to see the
theoretical ideas developed in a not too formal manner. But I hope it
may be of interest to students and research workers in related fields.
I assume no previous knowledge of the theory of thermal neutron
scattering, but a familiarity with the basic concepts of quantum
mechanics and solid state physics is necessary for a proper under-
standing of the text. The required results in these subjects are sum-
marized in appendices. The latter also contain proofs of some of the
mathematical results.
Some problem examples have been given at the ends of chapters.
They are intended to illustrate the text, and the reader is advised to
glance at them even if he is not inclined to try to solve them. Their
purpose is partly, as with some of the appendices, to remove some
mathematical material from the main body of the text, and partly, to
stimulate the reader to a more active understanding of the subject.
Thermal neutron scattering is being applied in more and more
areas of science. But this book does not attempt to cover the theory
of all the applications. Instead I have confined myself to the basic
ideas of the theory. My aim is to bring the reader to the point where
he can tackle the theoretical expositions of the specialized branches
given in more advanced textbooks and in theoretical papers.
It is a pleasure to thank Mr Cole, Dr Dore, Dr Howie, Professor
Joannopoulos, Dr de Vallera, and Dr Zeilinger for reading parts of the
manuscript and making useful comments.
Author(s): G.L. Squires
Publisher: Dover
Year: 1996
Language: English
Pages: 272
City: Mineola, NY USA
Preface ix
1 Introduction
1.1 Basic properties of the neutron 1
1.2 Numerical values for velocity, energy, wavelength 2
1.3 Definitions of scattering cross-sections 5
1.4 Scattering of neutrons by a single fixed nucleus 7
2 Nuclear scattering - basic theory
2.1 Introduction 10
2.2 Fermi's golden rule 10
2.3 Expression for d 2 u/dO dE' 13
2.4 Coherent and incoherent scattering 21
3 Nuclear scattering by crystals
3.1 Introduction 25
3.2 Normal modes 26
3.3 Probability function for a harmonic oscillator 27
3.4 Development of (exp U exp V) 28
3.5 Phonon expansion 30
3.6 Coherent elastic scattering 32
3.7 Coherent one-phonon scattering 43
3.8 Coherent multiphonon scattering 53
3.9 Incoherent scattering 54
3.10 Multiphonon cross-sections - approximation methods 57
Examples 59
4 Correlation functions in nuclear scattering
4.1 Definitions of I(K, t), G(r, t), and S(Ie, w) 61
4.2 Expressions for G(r, t) and Gs(r, t) 63
4.3 Analytic properties of the correlation functions 65
4.4 Principle of detailed balance 68
4.5 Scattering from a single free nucleus 70
4.6 Moments of the scattering function 73
4.7 Relation between elastic scattering and I (Ie, 00), G (r, CX)) 75
4.8 Static approximation 78
Examples 84
5 Scattering by liquids
5.1 Introduction 86
5.2 No elastic scattering 87
5.3 Coherent scattering 88
5.4 Incoherent scattering 96
6 Neutron optics
6.1 Refractive index 110
6.2 Neutron reflection 114
6.3 Dynamical theory of scattering 116
Examples 128
7 Magnetic scattering - basic theory
7.1 Preliminary results 129
7.2 Expression for d 2 u/ dO dE' 131
7.3 Scattering due to spin only 137
7.4 Scattering by ions with spin and orbital angular momentum 139
7.5 Time-dependent operators 139
7.6 Cross-section for a paramagnet 143
Examples 144
8 Scattering from magnetically ordered crystals
8.1 Elastic magnetic scattering 146
8.2 Scattering by spin waves 155
Examples 169
9 Polarization analysis
9.1 Introduction 171
9.2 Nuclear scattering 172
9.3 Magnetic scattering 177
9.4 Bragg scattering from magnetically ordered crystals 181
9.5 Scattering by the atomic electric field 188
Examples 194
Appendices
A The Dirac delta function 196
B Fourier transforms 201
C Some results for linear operators and matrix elements 204
D Heisenberg operators 207
E The harmonic oscillator in quantum mechanics 210
F Angular momentum in quantum mechanics 215
G Normal modes of crystals 218
H The proofs of two results for magnetic scattering 226
I Some mathematical results 229
Solutions to examples 231
Bibliography 241
References 243
Glossary of symbols 247
Index 255
