Handbook of Neutron Optics

Neutron Optics......Page 2
Contents......Page 8
Preface......Page 18
Textbooks......Page 22
1.1 Discovery of Matter Waves......Page 24
1.2.1 Bragg Reflection......Page 26
1.2.2 Refractive Index and Total Reflection......Page 28
1.2.3 Fraunhofer Diffraction......Page 31
1.2.4 Fresnel Diffraction......Page 34
1.3.1 Coherence Lengths......Page 36
1.3.2 Pendellösung Interference......Page 38
1.4.1 Time-of-Flight Analysis......Page 39
1.4.2 From a Particle to a Wave......Page 42
1.5.1 Spin Flip in Magnetic Resonance......Page 45
1.5.2 Adiabatic Spin Reversal in a Magnetic Gradient......Page 48
2.1.1 Measurement of Coherent Scattering Amplitude......Page 54
2.1.2 Neutron Guide Tube......Page 56
2.1.3 Total Reflection Potential and Surface Impurities......Page 57
2.1.4 Neutron Reflectometry......Page 62
2.2.1 Reflection Loss Probability......Page 66
2.2.2 Neutron Storage Bottle and Anomalous Loss Coefficient......Page 68
2.2.3 Limiting Velocity for Total Reflection and Neutron Absorption......Page 71
2.3.1 Developments of Multilayer Mirrors and Reflectivity Analyses......Page 74
2.3.2 High-Performance Supermirrors......Page 78
2.4.1 Neutron Turbine......Page 80
2.4.2 Fizeau Experiment......Page 85
2.5.1 Neutron Reflection and Transmission Experimentswith Macroscopic Resonators......Page 87
2.5.2 Nuclear Reaction Experiments of Neutrons......Page 90
3.1.1 Magnetic Reflection and Neutron Polarization......Page 94
3.1.2 Polarized Neutron Reflectometry......Page 97
3.1.3 Magnetic Storage of Neutrons......Page 100
3.2.1 Reflectivity Analyses with the Transfer Matrix Method......Page 104
3.2.2 Analyses of Nonspecular Reflections......Page 108
3.3 Neutron Behavior in Magnetic Devices......Page 110
3.3.1 Magnetic Deceleration and Acceleration of Neutrons......Page 111
3.3.2 Magnetic Focusing......Page 113
3.3.3 Pseudomagnetic Prism......Page 117
3.4.1 4 Periodicity of Spinor......Page 119
3.4.2 Coherent Superposition of Spin States......Page 122
3.5.1 Neutron Resonance Spin Echo Method......Page 126
3.5.2 Neutron Spin Maser......Page 130
3.6 Berry\'s Geometrical Phase......Page 131
4.1 Some Descriptions of the Fundamental Theory......Page 136
4.2 Reflection and Refraction at a Potential Step......Page 138
4.2.2 Optical Potential and Ultracold Neutrons......Page 140
4.2.3 Digression on the Ultracold Neutron Anomaly......Page 141
4.2.4 Experience with an Experiment......Page 144
4.2.5 Surface Waves......Page 149
4.2.6 Goos--Hänchen Shift......Page 150
4.3 Scattering by a Rectangular Potential Barrier......Page 152
4.3.1 The Other Method......Page 153
4.3.2 Asymptotical Behavior of Reflectivity from a Rectangular Barrier......Page 154
4.4 Neutron Scattering from Semitransparent Mirrors......Page 155
4.4.1 Bringing Two Mirrors Together......Page 156
4.4.4 Experience with an Experiment......Page 157
4.4.5 Properties of the Reflection and Transmission Amplitudes......Page 159
4.5 Periodic Systems......Page 161
4.5.2 Kronig--Penney Potential......Page 164
4.5.3 Supermirrors......Page 167
4.5.4 Experience with an Experiment......Page 175
4.6.1 Resonant Transmission......Page 178
4.6.2 Channeling......Page 182
4.6.3 Bound States in Periodic Potentials......Page 188
4.7 Potentials of General Form......Page 190
4.7.1 Analytical Description of Reflection from a Combinationof a Rectangular Barrier and Eckart Potentials......Page 191
4.7.2 Continuous-Fractions Method......Page 197
4.7.3 Matrix Method for Scattering from an Arbitrary Potential......Page 198
4.7.4 Perturbation Theory......Page 199
4.7.5 Reflection from Mirrors in an External Field......Page 200
4.8 Some Experiments with Moving Mirrors......Page 201
4.8.1 Uniform Motion......Page 202
4.8.2 Accelerating Mirror......Page 205
4.8.3 Vibrating Mirror......Page 211
4.8.4 Diffraction by a Moving Grating......Page 212
4.9 Conclusion......Page 213
5 One-Dimensional Scattering of Neutrons with Spin......Page 214
5.1.1 Plane Wave in a Homogeneous Magnetic Field......Page 216
5.1.2 Solution of Eq. (5.9)......Page 217
5.1.3 Triple Splitting of the Reflected Beam......Page 221
5.2.1 Magnetic Mirror of Finite Thickness......Page 224
5.2.2 System of Two Magnetic Mirrors......Page 225
5.2.4 Periodic System of Mirrors......Page 226
5.2.5 A Periodic Potential with Collinear Internal Fields......Page 227
5.2.6 Reflection from Helical Systems......Page 228
5.3 Numerical Matrix Method for Multilayered Magnetic Systems......Page 236
5.4.1 Polarizers......Page 238
5.4.3 Spin Rotators with Direct Current Fields......Page 239
5.4.4 Resonant Spin Rotators......Page 241
5.5 The Berry Phase......Page 247
5.6.1 Presumable Form of the Wave Function......Page 250
5.6.2 The Krüger Problem......Page 252
5.7.1 Spin Wave and Intensity Modulated Wave after a /2-Spin Flipper......Page 258
5.7.2 -Flipper......Page 262
5.8.1 General Principles of Holography......Page 270
5.8.2 Spin Precession Wave......Page 273
5.8.3 Hologram of a Scattered SPW without a Reference Wave......Page 275
5.8.4 Magnetic Scattering of a SPW with Spin Flip......Page 276
5.8.5 Entangled States. A Fundamental Question of Quantum Mechanics......Page 277
5.9 Conclusion......Page 278
6.1.1 Borrmann Effect......Page 280
6.1.2 Darwin Table......Page 283
6.2.1 Reflection and Transmission Formulas for a Thick Sample......Page 288
6.2.2 Measurements of Inhomogeneity Scatteringin the Long--Wavelength Region......Page 289
6.3 Small-Angle Scattering......Page 291
6.3.1 Analysis of the Guinier--Preston Zone......Page 294
6.3.2 Separation of Nuclear and Magnetic Structures......Page 297
6.3.3 Developments of Small Angle Scattering Spectrometers......Page 298
6.4.1 Quantum Shutter Analysis......Page 300
6.4.2 Fame-Overlapping Time-of-Flight Quantum-Chopper Spectrometer......Page 303
6.5.1 Discovery of the Basic Idea of Holography......Page 306
6.5.2 Theoretical Principle of Wave Front Reconstruction......Page 308
6.5.3 Neutron Holography Experiment......Page 310
7 Dynamical Diffraction in Three-dimensional Periodic Media......Page 314
7.1 Diffraction on a Single Crystalline Plane......Page 315
7.1.2 Scattering on an Infinite Crystalline Plane......Page 316
7.1.3 Scattered Field of the Crystalline Plane......Page 317
7.1.4 An Idea for Calculation of S......Page 319
7.2 Diffraction from a Semi-infinite Single Crystal......Page 322
7.2.1 Properties of Dyadic Matrices......Page 323
7.2.2 Solution of Eq. (7.34)......Page 324
7.2.3 Bragg Diffraction......Page 326
7.3 Diffraction on a Crystal of Finite Thickness......Page 330
7.3.1 Eigenvectors and Eigenvalues of the Operator bold0mu mumu file:///diamond/dtd/wileyml21/wileyml21.dtd......Page 331
7.3.3 Two Values of en Are Close to each other......Page 333
7.3.4 The Bloch Wave Vector at a Specular Bragg Diffraction......Page 335
7.3.5 Specular Bragg Diffraction......Page 336
7.3.6 Total Reflection of a Mosaic Crystal......Page 337
7.3.7 Extinction Coefficients......Page 339
7.3.8 The Laue Diffraction......Page 341
7.4.1 The Fermi Pseudopotential......Page 344
7.4.2 The Standard Dynamical Diffraction Theory......Page 345
7.5 Comparison of the Two Methods......Page 348
7.6 Kinematical Diffraction Theory and Practical Crystallography......Page 349
7.7 Unitarity and the Detailed Balance Principle......Page 351
7.7.1 Unitarity......Page 352
7.7.2 The Detailed Balance Principle......Page 353
7.8 The Optical Potential u0......Page 355
7.8.1 Kronig--Penney Corrections to the Optical Potential......Page 356
7.8.2 Diffraction Correction to the Optical Potential......Page 357
7.8.3 Digression on the Optical Potential......Page 358
7.9 Conclusion......Page 361
8.1.1 Equations of MWS......Page 362
8.1.2 Solution for Coherent Values......Page 364
8.1.3 Renormalization of the Scattering Amplitude......Page 366
8.2 Scattering......Page 367
8.2.1 Propagation of Scattered Waves inside the Medium......Page 369
8.2.2 Scattering with the Modified Green Function......Page 370
8.2.3 Experience with an Experiment......Page 378
8.2.4 Small-Angle Scattering on a Single Inhomogeneityinside the Medium......Page 379
8.2.5 Small-Angle Scattering on a Set of Inhomogeneities......Page 383
8.2.6 Scattering on Roughnesses at the Interface......Page 385
8.3 Scattering on Magnetic Inhomogeneities......Page 391
8.3.1 The Spinor Green Function......Page 392
8.3.2 The Scattered Wave Function......Page 394
8.4.1 Main Notions......Page 399
8.4.2 Albedo of an Infinitely Thick Wall......Page 400
8.4.4 Albedo of a Wall of Thickness L......Page 403
8.4.5 Comparison with Diffusion Formulas for the Albedo......Page 404
8.4.6 Albedo of Ultrathin Powdered Matter......Page 405
8.4.7 Angular Distribution of Reflected Neutrons for Isotropic Scattering......Page 406
8.4.8 Angular Distribution for Anisotropic Scattering......Page 407
8.5 Conclusion......Page 410
9 Neutron Interference and Phase Observation......Page 412
9.1.1 Triple Laue Diffraction Type Silicon Crystal Interferometer......Page 413
9.1.2 Experimental Verification of the Equivalence Principleon the Gravity Effect......Page 415
9.1.3 Coherence Length and Dispersive/Nondispersive Arrangements......Page 419
9.1.4 Stochastic and Deterministic Processes in the Absorbing Element......Page 422
9.1.5 Study of Quantum Entangled Stateswith a Skew--Symmetrical Perfect Crystal Interferometer......Page 425
9.2.1 4 Periodicity of Spin Precession in a Magnetic Field......Page 427
9.2.2 Complementary Principle in a Double-Resonance Experiment......Page 428
9.2.3 Experimental Test of the Einstein--Podolsky--Rosen Paradox......Page 432
9.3.1 Development of a Grating Mirror Interferometerand Experiment on the Gravity Effect......Page 436
9.3.2 Experimental Verification of Aharonov--Bohm Effect......Page 439
9.4 Time-Dependent Interferometry......Page 443
9.5 Neutron Interferometry with Single-Layer and Multilayer Mirrors......Page 445
9.6.1 Development of a Phase-Spin-Echo Interferometer......Page 449
9.6.2 Observation of the Transverse Coherence Length......Page 451
9.6.3 Observation of Quasi-Bound States of the Neutronin a Magnetic Resonator......Page 454
9.6.4 Observation of Larmor Precession on Resonant Tunneling Neutrons......Page 458
9.6.5 Experimental Test of Wave Packet Theorieswith Very Cold Neutron Interferometry......Page 460
10.1 How many Scattering Theories Do We Have?......Page 468
10.1.1 Theory of Spherical Waves......Page 469
10.2.1 Scattering of Spherical Waves......Page 470
10.2.2 Cross Section in the Standard Theory......Page 472
10.2.3 Fundamental Scattering Theory [457,458]......Page 473
10.3.1 Phenomenological Definition of the Cross Sectionin the Self-Consistent Theory of Spherical Waves......Page 475
10.3.2 Relation between Cross Section and Probability......Page 476
10.4 Wave Packets......Page 478
10.4.2 Estimation of s......Page 479
10.4.4 Resolution of Contradiction 6. Quantization of the Scattering Angle......Page 480
10.5 Details......Page 482
10.5.1 Main Points of the Fundamental Scattering TheoryAccording to [457,458]......Page 483
10.5.2 Elastic Scattering of a Wave Packet on a Fixed Center......Page 485
10.5.3 Transition from Probabilities to Cross Sections......Page 486
10.6.1 The EPR Paradox, Its Logic, Error, and Consequences......Page 488
10.6.2 Interpretation of Quantum Mechanics and Hidden Variables......Page 499
10.6.3 Discussion of some Experiments with Wave Packets......Page 501
10.7 Modern Art in Neutron Optics......Page 502
10.8 Conclusion......Page 505
11.1 Nuclear Scattering Density Profile Analyses of Layered Materials......Page 508
11.2.1 Penetration Depth in Superconductors......Page 510
11.2.2 Reference Layer Methods for Multilayers......Page 515
11.2.3 Nonspecular Reflection from Magnetic Multilayers......Page 516
11.2.4 Magnetic Materials with Artificial Properties......Page 517
11.3.1 Graphite Inhomogeneity Structure Observedwith Very Cold Neutrons......Page 521
11.3.2 Solid Water Inhomogeneity Structures Observed with Coldand Very Cold Neutrons......Page 523
11.3.3 Mechanically Alloyed Graphite Structure Observedwith Neutron Diffraction......Page 527
11.4.1 Observation of Spinodal Decomposition......Page 529
11.4.2 Precipitation and Segregation in an Alloy......Page 531
11.5.1 Matter under Pressure. Stress and Strain......Page 532
11.5.2 Texture of Matter......Page 533
11.5.3 Small-Angle Neutron Scattering......Page 536
11.5.4 Neutron Radiography......Page 537
11.5.5 Phase-Contrast Neutron Radiography......Page 540
11.6 An Example of Novel Applications of Spin Echo Spectrometry -- Study on Dairy Products......Page 545
12 Application of Neutron Optics in Biophysical/Biological Research......Page 550
12.1 Contrast Variation......Page 551
12.1.1 Isotope Substitution......Page 552
12.1.2 Spin Contrast Variation......Page 554
12.2 Scattering from a Dilute Ensemble of Monoparticles......Page 556
12.2.1 Properties of (bold0mu mumu rrfile:///diamond/dtd/wileyml21/wileyml21.dtdrrrr)......Page 558
12.2.2 Properties of I(q)......Page 559
12.2.3 Some Special Forms of Particles......Page 560
12.3 Multipole Expansion of the Scattering Density......Page 562
12.3.1 Derivation of Eq. (12.54)......Page 564
12.4.1 Guinier Region. Scattering from a Dilute Monoparticle Solution......Page 565
12.4.2 Small-Angle Scattering from a Systemof Two and more Different Particles......Page 569
12.5.1 A New Tool to Study Protein Interactions......Page 571
12.5.2 Membrane Investigations......Page 572
12.6 Diffraction on Biological Macromolecules......Page 574
12.7 Neutron Microscope for Biological Samples......Page 576
Basic Formulas in Neutron Optics......Page 580
References......Page 582
Index......Page 606