Introduction to the Theory of Thermal Neutron ScatteringGraduate-level monograph develops theoretical ideas in a relatively informal manner. Nuclear scattering, nuclear scattering by crystals, scattering by liquids, neutron optics, polarization analysis, much more. Problem examples at chapter ends. Prerequisites are some familiarity with basic concepts of quantum mechanics and solid state physics. Solutions. Bibliography. Appendixes. 1978 edition. |
Contents
Introduction | 1 |
12 Numerical values for velocity energy wavelength | 2 |
13 Definitions of scattering crosssections | 5 |
14 Scattering of neutrons by a single fixed nucleus | 7 |
Nuclear scatteringbasic theory | 10 |
23 Expression for d2σdΩdE | 13 |
24 Coherent and incoherent scattering | 21 |
Nuclear scattering by crystals | 25 |
62 Neutron reflection | 114 |
63 Dynamical theory of scattering Basic theory | 116 |
Examples | 128 |
Magnetic scatteringbasic theory | 129 |
72 Expression for d2σdΩdE | 131 |
74 Scattering by ions with spin and orbital angular momentum | 139 |
76 Crosssection for a paramagnet | 143 |
Examples | 144 |
32 Normal modes | 26 |
33 Probability function for a harmonic oscillator | 27 |
34 Development of exp U exp V | 28 |
35 Phonon expansion | 30 |
36 Coherent elastic scattering | 32 |
37 Coherent onephonon scattering | 43 |
38 Coherent multiphonon scattering | 53 |
39 Incoherent scattering | 54 |
310 Multiphonon crosssections approximation methods | 57 |
Examples | 59 |
Correlation functions in nuclear scattering | 61 |
42 Expressions for Gr t and Gr t | 63 |
43 Analytic properties of the correlation functions | 65 |
44 Principle of detailed balance | 68 |
45 Scattering from a single free nucleus | 70 |
46 Moments of the scattering function | 73 |
47 Relation between elastic scattering and IK Gr | 75 |
48 Static approximation | 78 |
Examples | 84 |
Scattering by liquids | 86 |
52 No elastic scattering | 87 |
53 Coherent scattering | 88 |
54 Incoherent scattering | 96 |
Neutron optics | 110 |
Scattering from magnetically ordered crystals | 146 |
82 Scattering by spin waves | 155 |
Examples | 169 |
Polarisation analysis | 171 |
92 Nuclear scattering | 172 |
93 Magnetic scattering | 177 |
94 Bragg scattering from magnetically ordered crystals | 181 |
95 Scattering by the atomic electric field | 188 |
Examples | 194 |
The Dirac delta function | 196 |
Fourier transforms | 201 |
Some results for linear operators and matrix elements | 204 |
Heisenberg operators | 207 |
The harmonic oscillator in quantum mechanics | 210 |
Angular momentum in quantum mechanics | 215 |
Normal modes of crystals | 218 |
The proofs of two results for magnetic scattering | 226 |
Some mathematical results | 229 |
SOLUTIONS TO EXAMPLES | 231 |
| 241 | |
REFERENCES | 243 |
GLOSSARY OF SYMBOLS | 247 |
| 255 | |
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Common terms and phrases
angle angular momentum Appendix atom axis Bragg peak Bragg scattering Bravais crystal calculate classical coherent one-phonon component Consider constant corresponding cubic curve Debye-Waller factor defined density direction displacement eigenfunctions eigenvalues elastic scattering electron energy equation exp(−iwt exp(ik expression factor ferromagnet Fourier transform frequency geometry gives Hamiltonian incident neutrons incoherent scattering inelastic integrating with respect interaction INTRODUCTION ions liquid magnetic field magnetic scattering mathematical matrix element measurements neutrons scattered normal modes nuclear scattering nuclear spin nucleus obtained one-phonon scattering orbital particle perfect gas phonon Phys physical plane polarisation position potential problems quantity quantum mechanics quantum number R₁ reciprocal lattice scattered neutrons scattering function scattering length scattering system shown in Fig space spin wave spin-flip spin-state static approximation surface temperature term theory thermal average thermal neutrons unit cell vector velocity wavelength wavevector zero ΦΩ