Diffraction effects in semiclassical scattering

Cover......Page 1
Title page......Page 6
Copyright......Page 7
Contents......Page 8
Preface......Page 12
1.1 Classical scattering......Page 16
1.2 Semiclassical scattering......Page 21
1.3 Critical effects......Page 26
2.1 Geometrical optics......Page 30
2.2 Classical diffraction theory......Page 32
2.3 The corona......Page 35
3.1 Geometrical-optic theory......Page 37
3.2 Wave-optic theory......Page 40
3.3 Electromagnetic theory......Page 44
4.1 Observations......Page 45
4.2 Proposed theories......Page 47
4.3 The geometrical theory of diffraction......Page 49
5.1 The Mie solution......Page 52
5.2 Convergence difficulties......Page 55
5.3 Lasing droplets......Page 58
6.1 The Poisson representation......Page 60
6.2 CAM approximations......Page 63
7.1 WKB and classical diffraction theory approximations......Page 67
7.2 Geometrical theory of diffraction......Page 70
7.3 Fock\'s theory of diffraction......Page 72
7.4 CAM theory......Page 75
7.5 Structure of the hard sphere wave function......Page 79
8 Diffraction as tunneling......Page 83
8.1 Effective potential and edge domain......Page 84
8.2 Reinterpretation of the Fock theory......Page 86
8.3 Outer and inner representations......Page 87
8.4 The CAM approximation......Page 89
8.5 The Fock approximation......Page 93
8.6 Numerical comparisons......Page 94
8.7 Diffraction as a tunneling effect......Page 98
9.1 The effective potential......Page 102
9.2 Regge poles......Page 104
9.3 The Debye expansion......Page 105
9.4 Convergence of the Debye expansion......Page 108
9.5 Direct reflection term......Page 110
9.6 Direct transmission term......Page 112
10.1 The third Debye term......Page 116
10.2 The Chester-Friedmann-Ursell method......Page 120
10.3 Uniform CAM rainbow approximation......Page 122
10.4 CAM rainbow theory predictions......Page 124
10.5 Numerical tests......Page 127
10.6 Rainbow as a diffraction catastrophe......Page 130
11.1 Observational and numerical glory features......Page 132
11.2 Cross-polarization and axial focusing......Page 136
11.3 Geometrical-optic and van de Hulst terms......Page 139
11.4 Orbiting and leading higher-order terms......Page 143
11.5 CAM theory of the glory......Page 149
11.6 Explanation of the glory features......Page 152
12 Near-critical scattering......Page 158
12.1 Geometrical-optic theory......Page 159
12.2 Removal of fine structure......Page 160
12.3 Interference and physical optics theories......Page 162
12.4 Effective potential and leading CAM terms......Page 166
12.5 CAM theory of near-critical scattering......Page 167
12.6 Planar reflection limit and Goos-Hanchen shift......Page 170
12.7 Numerical comparisons......Page 174
13.1 Efficiency factors......Page 179
13.2 CAM theory of average efficiency factors......Page 182
13.3 Numerical results......Page 185
13.4 Forward optical glory......Page 188
14 Orbiting and resonances......Page 193
14.1 Effective potential and resonances......Page 194
14.2 The poles of the S-function......Page 196
14.3 Resonance and background contributions......Page 198
14.4 CAM theory of the ripple......Page 200
15.1 Recent applications of Mie scattering......Page 205
15.2 Applications to radiative transfer and to astronomy......Page 208
15.3 Applications to acoustics......Page 213
15.4 Applications to seismology......Page 214
15.5 Nonlinear Mie scattering......Page 216
16.1 Atomic diffractive and rainbow scattering......Page 219
16.2 Atomic glories and orbiting resonances......Page 222
16.3 Rainbows in nuclear physics......Page 224
16.4 Nuclear glories and surface waves......Page 227
16.5 Application to particle physics......Page 232
16.6 Why complex angular momentum?......Page 234
References......Page 236
Index......Page 246