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Scattering of Electromagnetic Waves | p. 1 |
Formalism and General Results | p. 3 |
The Maxwell Equations | p. 3 |
Stokes Parameters and Polarization | p. 4 |
Definition of the Stokes Parameters | p. 4 |
Significance of the Parameters | p. 6 |
Partially Polarized Beams | p. 8 |
Stokes Vectors | p. 9 |
Relation to the Density Matrix | p. 10 |
Scattering | p. 11 |
The Scattering Amplitude | p. 11 |
Change to a Reference Plane through a Fixed Direction | p. 12 |
Relation of Circular to Linear Polarization Components in the Scattering Amplitude | p. 12 |
Stokes Vectors of the Scattered Wave | p. 13 |
The Differential Cross Section | p. 14 |
The Density Matrix of the Scattered Wave | p. 15 |
Azimuthal Dependence of Forward and Backward Scattering | p. 16 |
Effects of Rotational or Reflectional Symmetry | p. 16 |
Forward Scattering; the Optical Theorem | p. 18 |
Double Scattering | p. 20 |
Scattering by a Cloud of Many Particles | p. 23 |
Addition of Cross Sections | p. 23 |
Index of Refraction | p. 24 |
More than One Kind of Particle | p. 26 |
Notes and References | p. 27 |
Problems | p. 28 |
Spherically Symmetric Scatterers | p. 30 |
Spherical Harmonics | p. 30 |
Legendre Polynomials | p. 30 |
Associated Legendre Functions | p. 31 |
Spherical Harmonics | p. 31 |
Vector Spherical Harmonics | p. 32 |
Transverse and Longitudinal Vector Spherical Harmonics | p. 34 |
Rotationally Invariant Tensor Functions | p. 35 |
Complex Conjugation Properties | p. 36 |
[theta] and [phi] Components | p. 36 |
The z Axis along r | p. 37 |
Multipole Expansions | p. 38 |
Expansion of a Plane Wave; Spherical Bessel Functions | p. 38 |
Expansion of the Electric Field | p. 40 |
The Magnetic Field | p. 41 |
The [characters not reproducible] Matrix | p. 42 |
The Scattering Amplitude | p. 42 |
The z Axis along k | p. 42 |
Unitarity and Reciprocity | p. 44 |
Energy Conservation and Unitarity | p. 44 |
Phase Shifts | p. 45 |
Time Reversal and Reciprocity | p. 46 |
The Generalized Optical Theorem | p. 47 |
Generalization to Absence of Spherical Symmetry | p. 48 |
Scattering by a Uniform Sphere (Mie Theory) | p. 48 |
Calculation of the [characters not reproducible] Matrix | p. 48 |
The Scattering Amplitude | p. 50 |
Notes and References | p. 51 |
Problems | p. 52 |
Limiting Cases and Approximations | p. 54 |
Small Spheres, Not Too Dense (Rayleigh Scattering) | p. 54 |
Low Optical Density, Not Too Large (Rayleigh-Gans; Born Approximation) | p. 56 |
Small Dense Spheres | p. 61 |
Resonance Scattering | p. 61 |
Totally Reflecting Spheres | p. 65 |
Large Diffuse Spheres (Van de Hulst Scattering) | p. 66 |
Forward Scattering | p. 66 |
Small-Angle Scattering | p. 69 |
Large Spheres (Geometrical-Optics Limit) | p. 70 |
Fraunhofer Diffraction | p. 71 |
Nonforward and Nonbackward Scattering; Real Index of Refraction | p. 72 |
Large Diffuse Spheres | p. 76 |
Large Dense Spheres | p. 77 |
Complex Index of Refraction | p. 77 |
The Rainbow | p. 78 |
The Glory | p. 82 |
Grazing Rays (The Watson Method) | p. 83 |
The Watson Transform | p. 84 |
Convergence Questions | p. 90 |
Saddle-Point Integration (The Method of Steepest Descent) | p. 94 |
Notes and References | p. 96 |
Problems | p. 96 |
Miscellaneous | p. 98 |
Other Methods | p. 98 |
Debye Potentials | p. 98 |
The Green's-Function Method | p. 100 |
Causality and Dispersion Relations | p. 103 |
Introduction | p. 103 |
Forward-Dispersion Relations | p. 104 |
Nonforward-Dispersion Relations | p. 107 |
Partial-Wave-Dispersion Relations | p. 109 |
Intensity-Fluctuation Correlations (Hanbury Brown and Twiss Effect) | p. 110 |
Notes and References | p. 116 |
Problems | p. 117 |
Additional References for Part I | p. 118 |
Scattering of Classical Particles | p. 119 |
Particle Scattering in Classical Mechanics | p. 121 |
The Orbit Equation and the Deflection Angle | p. 121 |
The Nonrelativistic Case | p. 121 |
The Relativistic Case | p. 123 |
The Scattering Cross Section | p. 124 |
The Rutherford Cross Section | p. 126 |
Orbiting (Spiral Scattering) | p. 127 |
Glory and Rainbow Scattering | p. 129 |
Singular Potentials | p. 130 |
Transformation Between Laboratory and Center-of-Mass Coordinate Systems | p. 132 |
Indentical Particles | p. 136 |
The Inverse Problem | p. 137 |
Notes and References | p. 139 |
Problems | p. 140 |
Quantum Scattering Theory | p. 141 |
Time-Dependent Formal Scattering Theory | p. 143 |
The Schrodinger Equation | p. 145 |
Time Development of State Vectors in the Schrodinger Picture | p. 146 |
The Moller Wave Operator in the Schrodinger Picture | p. 151 |
The S Matrix | p. 156 |
The Interaction Picture | p. 158 |
The Heisenberg Picture | p. 160 |
Scattering into Cones | p. 162 |
Mathematical Questions | p. 164 |
Convergence of Vectors | p. 164 |
Operator Convergence | p. 166 |
Convergences in the Schrodinger Picture | p. 169 |
The Limits in the Interaction Picture | p. 171 |
The Limits in the Heisenberg Picture | p. 172 |
Notes and References | p. 172 |
Problems | p. 174 |
Time-Independent Formal Scattering Theory | p. 175 |
Green's Functions and State Vectors | p. 176 |
The Green's Functions | p. 176 |
The State Vectors | p. 178 |
Expansion of the Green's Functions | p. 181 |
The Wave Operator and the S Matrix | p. 182 |
The Operators [Omega], S, and S' | p. 182 |
The T Matrix | p. 183 |
The K Matrix | p. 187 |
Unitarity and Reciprocity | p. 189 |
Additive Interactions | p. 191 |
Mathematical Questions | p. 194 |
The Spectrum | p. 195 |
Compact Operators | p. 198 |
Hermitian and Unitary Operators | p. 200 |
Analyticity of the Resolvent | p. 204 |
Appendix | p. 208 |
Notes and References | p. 208 |
Problems | p. 209 |
Cross Sections | p. 211 |
General Definition of Differential Cross Sections | p. 211 |
Relativistic Generalization | p. 215 |
Scattering of Incoherent Beams | p. 217 |
The Density Matrix | p. 217 |
Particles with Spin | p. 221 |
The Cross Section and the Density Matrix of the Scattered Wave | p. 225 |
Notes and References | p. 226 |
Problems | p. 227 |
Formal Methods of Solution and Approximations | p. 228 |
Perturbation Theory | p. 228 |
The Born Series | p. 228 |
The Born Approximation | p. 238 |
The Distorted-Wave Born Approximation | p. 239 |
Bound States from the Born Approximation | p. 240 |
The Schmidt Process (Quasi Particles) | p. 241 |
The Fredholm Method | p. 247 |
Singularities of an Operator Inverse | p. 255 |
Notes and References | p. 257 |
Problems | p. 258 |
Single-Channel Scattering (Three-Dimensional Analysis in Specific Representations) | p. 260 |
The Scattering Equation in the One-Particle Case | p. 260 |
Preliminaries | p. 260 |
The Coordinate Representation | p. 261 |
The Momentum Representation | p. 266 |
Separable Interactions | p. 268 |
The Scattering Equations in the Two-Particle Case (Elimination of Center-of-Mass Motion) | p. 270 |
Three-Dimensional Analysis of Potential Scattering | p. 273 |
Born Series | p. 274 |
Fredholm Theory | p. 277 |
Scattering Amplitude, Cross Section, and S Matrix | p. 282 |
Dispersion Relations | p. 289 |
An Example (the Yukawa Potential) | p. 291 |
Notes and References | p. 295 |
Problems | p. 297 |
Single-Channel Scattering of Spin 0 Particles, I | p. 298 |
Partial-Wave Expansion | p. 298 |
The S Matrix and Traveling Waves | p. 298 |
The K Matrix and Standing Waves | p. 303 |
Time Delay | p. 304 |
Heuristic Survey of Phase-Shift Behavior | p. 305 |
General Properties | p. 305 |
Discussion of Low-Energy Phase-Shift Behavior | p. 306 |
Variational Approaches | p. 318 |
General Introduction | p. 318 |
The T Matrix, K Matrix, and the Green's Function | p. 319 |
Variational Formulations of the Phase Shift | p. 321 |
The s-Wave Scattering Length | p. 322 |
Proof of the Hylleraas-Undheim Theorem | p. 326 |
Notes and References | p. 327 |
Problems | p. 328 |
Single-Channel Scattering of Spin 0 Particles, II | p. 331 |
Rigorous Discussion of s-Wave Scattering | p. 331 |
The Regular and Irregular Solutions | p. 331 |
The Jost Function and the Complete Green's Function | p. 341 |
The S Matrix | p. 350 |
The Poles of S | p. 357 |
Completeness | p. 368 |
Higher Angular Momenta | p. 371 |
Continuous Angular Momenta | p. 380 |
Singular Potentials | p. 389 |
The Difficulties | p. 389 |
Singular Repulsive Potentials | p. 392 |
An Example | p. 394 |
Notes and References | p. 396 |
General References | p. 399 |
Problems | p. 399 |
The Watson-Regge Method (Complex Angular Momentum) | p. 402 |
The Watson Transform | p. 402 |
Uniqueness of the Interpolation | p. 408 |
Regge Poles | p. 410 |
The Mandelstam Representation | p. 412 |
Notes and References | p. 415 |
Problems | p. 416 |
Examples | p. 417 |
The Zero-Range Potential | p. 418 |
The Repulsive Core | p. 419 |
The Exponential Potential | p. 420 |
The Hulthen Potential | p. 421 |
Potentials of the Yukawa Type | p. 422 |
The Coulomb Potential | p. 424 |
The Pure Coulomb Field | p. 424 |
Coulomb Admixtures | p. 431 |
Bargmann Potentials and Generalizations | p. 433 |
General Procedure | p. 433 |
Special Cases | p. 437 |
Notes and References | p. 440 |
Problems | p. 441 |
Elastic Scattering of Particles with Spin | p. 444 |
Partial-Wave Analysis | p. 444 |
Expansion in j and s | p. 444 |
Amplitudes for Individual Spins | p. 450 |
Unitarity, Reciprocity, Time-Reversal Invariance, and Parity Conservation | p. 452 |
Special Cases | p. 457 |
Cross Sections | p. 459 |
Double Scattering | p. 460 |
Solution of the Coupled Schrodinger Equations | p. 461 |
The Matrix Equation | p. 461 |
Solutions | p. 462 |
Jost Matrix and S Matrix | p. 464 |
Bound States | p. 468 |
Miscellaneous Remarks | p. 471 |
Notes and References | p. 472 |
Problems | p. 472 |
Inelastic Scattering and Reactions (Multichannel Theory), I | p. 474 |
Descriptive Introduction | p. 474 |
Time-Dependent Theory | p. 477 |
The Schrodinger Picture | p. 477 |
The Heisenberg Picture | p. 482 |
Two-Hilbert-Space Formulation | p. 483 |
Time-Independent Theory | p. 485 |
Formal Theory | p. 485 |
Distorted-Wave Rearrangement Theory | p. 487 |
Identical Particles | p. 488 |
Large-Distance Behavior of the Two-Cluster Wave Function | p. 489 |
Partial-Wave Analysis | p. 492 |
The Coupled Equations | p. 492 |
The S Matrix | p. 494 |
Rearrangements | p. 495 |
General Scattering Rates | p. 495 |
Formal Resonance Theory | p. 500 |
Appendix | p. 508 |
Notes and References | p. 510 |
Problems | p. 513 |
Inelastic Scattering and Reactions (Multichannel Theory), II | p. 514 |
Analyticity in Many-Channel Problems | p. 514 |
The Coupled Equations | p. 514 |
An Alternative Procedure | p. 519 |
Analyticity Properties | p. 521 |
Bound States | p. 526 |
The Riemann Surface of the Many-Channel S Matrix | p. 528 |
Threshold Effects | p. 534 |
Threshold Branch Points | p. 534 |
Physical Threshold Phenomena; General Arguments | p. 538 |
Details of the Anomaly | p. 539 |
The Threshold Anomaly for Charged Particles | p. 544 |
Examples | p. 548 |
The Square Well | p. 548 |
Potentials of Yukawa Type | p. 551 |
The Wigner-Weisskopf Model | p. 553 |
The Three-Body Problem | p. 555 |
Failure of the Multichannel Method and of the Lippmann-Schwinger Equation | p. 555 |
The Faddeev Method | p. 558 |
Other Methods | p. 560 |
Fredholm Properties and Spurious Solutions | p. 563 |
The Asymptotic Form of Three-Particle Wave Functions | p. 565 |
Angular Momentum Couplings | p. 571 |
The S Matrix | p. 579 |
The Efimov Effect | p. 580 |
Notes and References | p. 581 |
Problems | p. 586 |
Short-Wavelength Approximations | p. 588 |
Introduction | p. 588 |
Diffraction from the Optical Theorem | p. 590 |
The WKB Method | p. 591 |
The WKB Phase Shifts | p. 591 |
The Scattering Amplitude | p. 594 |
The Rainbow | p. 597 |
The Glory | p. 598 |
Orbiting (Spiral Scattering) | p. 600 |
The Eikonal Approximation | p. 600 |
The Impulse Approximation | p. 605 |
Notes and References | p. 609 |
Problems | p. 611 |
The Decay of Unstable States | p. 612 |
Qualitative Introduction | p. 612 |
Exponential Decay and Its Limitations | p. 614 |
Multiple Poles of the S Matrix | p. 625 |
Notes and References | p. 626 |
Problems | p. 626 |
The Inverse Scattering Problem | p. 629 |
Introduction | p. 629 |
The Phase of the Amplitude | p. 633 |
The Central Potential Obtained from a Phase Shift | p. 637 |
The Gel'fand-Levitan Equations | p. 637 |
Infinitesimal Variations | p. 645 |
The Marchenko Equation | p. 648 |
The Central Potential Obtained from All Phase Shifts at One Energy | p. 650 |
The Construction Procedure | p. 650 |
Examples | p. 657 |
The Inverse Scattering Problem for Noncentral Potentials | p. 659 |
Introduction | p. 659 |
The Generalized Marchenko Equation | p. 659 |
A Generalized Gel'fand-Levitan Equation | p. 665 |
Potential Obtained from Backscattering | p. 666 |
Notes and References | p. 667 |
Problems | p. 670 |
Bibliography | p. 671 |
Index | p. 727 |
Errata | p. 745 |
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