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Adhikari S.K. — Variational Principles and the Numerical Solution of Scattering Problems |
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Anomalous behavior 134—136 215—219
Anomalous behavior in complex Kohn method 219
Anomalous behavior in inverse Kohn method 134—136
Anomalous behavior in Kohn method 134—136
Anomalous behavior in Newton method 217
Anomalous behavior in Schwinger method 216—217
Asymptotic, behavior of Green’s function 22 26
Asymptotic, behavior of Lippmann — Schwinger, equation 25—27
Asymptotic, behavior of spherical Bessel and, Neumann functions 15—16 26
Asymptotic, behavior of wave function 12 14 16—17 47 50
Asymptotic, boundary condition 11 14
Atom-diatom collision (reactive) 248—249 237—240 300—304
Atom-diatom collision (reactive), complex Kohn method 248—249 301 304
Atom-diatom collision (reactive), Newton method 237—240 300—304
Atomic unit 261
Basis functions, 5
Basis functions, Kohn method 115—116 138
Basis functions, Schwinger method 170—171
Born or Neumann (series) for bound state 92
Born or Neumann (series) for distorted wave 194
Born or Neumann (series) for scattering 69 80—84 160 256
Born or Neumann (series) for T matrix 79 83 213 269—271
Born or Neumann (series) for wave function 34
Born or Neumann (series), approximation 29—30 57 80
Bound-state, approximation 51
Bound-state, scattering approach, for 91—94
Channel 5—6
Channel, open 51
Close-coupling (CC) equations 9 43 49—54 63 85 225—226
Close-coupling (CC) equations for K matrix 56
Close-coupling (CC) equations for t matrix 53 227—229
Close-coupling (CC) equations for wave function 52
Close-coupling (CC) equations, electron-helium scattering 290
Close-coupling (CC) equations, electron-hydrogen scattering 284
Close-coupling (CC) equations, partial-wave 54—56
Close-coupling (CC) equations, positron-helium scattering 293
Close-coupling (CC) equations, positron-hydrogen scattering 286
Close-coupling (CC) equations, post 53—54
Close-coupling (CC) equations, prior 53—54
Collision 3 319
Contour deformation technique 68
Cross section, electron-helium scattering 291
Cross section, electron-hydrogen scattering 280
Cross section, multichannel 59—60
Cross section, partial-wave 18—20
Cross section, reaction 19
Cross section, total 20
Effective range 42
Electron-helium scattering 288—292
Electron-helium scattering, Bethe — Goldstone method 289
Electron-helium scattering, Born formula 291
Electron-helium scattering, close-coupling (CC) method 290
Harris method 282
Harris method, Born formula for phase shift 281
Harris method, close-coupling (CC) approach 281 284
Harris method, Electron-hydrogen scattering 280—285
Harris method, optimized anomaly-free method 289
Harris method, polarizability 290—291
Harris method, polarized-orbital method 289
Harris method, resonance 290—291
K matrix 36
K matrix, half-shell 77—78
K matrix, off-shell 159
K matrix, principal-value treatment 68 71—74 86
K matrix, unitarity 41
Kernel, compact 24 64
Kernel, Fredholm 24 43 50 63—69 76
Kernel, Hilbert — Schmidt 24 44
Kohn method 297
Kohn method for resonance 95—97
Kohn method, 299—300
Kohn method, complex Kohn method 298
Kohn method, continuum orbitals 249—253
Kohn method, degenerate-kernel method 106 179
Kohn method, Electron volt 261
Kohn method, Electron-molecule scattering 297—300
Kohn method, Faddeev — Yakubovskii equation 9 40
Kohn method, Feshbach projection operator technique, Kohn method 190
Kohn method, Fock coupling scheme 50
Kohn method, Fredholm 7 62—69 76 79
Kohn method, Green’s function, incoming-wave 22—23
Kohn method, Hartree — Fock, wave function 249—250
Kohn method, Huck model 272
Kohn method, hydrogen 297—298
Kohn method, i?-matrix method 297—299
Kohn method, Integral equation 7
Kohn method, Integration quadratures 66 72
Kohn method, Ionization 4
Kohn method, iterative Schwinger method 298 300
Kohn method, method of moments 103—104
Kohn method, multichannel 87—90
Kohn method, nitrogen 298
Kohn method, nonsingular 74—80
Kohn method, numerical results 280—285
Kohn method, outgoing-wave 22—23
Kohn method, phase shift 283
Kohn method, polarizability 281 283
Kohn method, polarized orbital method 282
Kohn method, principal-value 37—38 73
Kohn method, resonances 282—283
Kohn method, Schwinger (multichannel) method 297—300
Kohn method, Schwinger multichannel method 229—234
Kohn method, T matrix 8—9 74—80
Kohn method, variational principle 210—215
Kohn method, variational principles 101—107
Lippmann — Schwinger equation 7 21
Lippmann — Schwinger equation for K matrix 39 40
Lippmann — Schwinger equation for t matrix 28 31
Lippmann — Schwinger equation for wave function 23
Lippmann — Schwinger equation, (iterative) Born — Neumann series, solution 7—8 34 80
Lippmann — Schwinger equation, asymptotic behavior 25—27
Lippmann — Schwinger equation, multiparticle 43 49
Lippmann — Schwinger equation, nonuniqueness of solution 44 45
Lippmann — Schwinger equation, numerical solution 65—74
Moller operator 12
Neumann series (see “Born series”)
Newton method 267—268 276—277 300—304
Newton method, nucleon-nucleon scattering 275—278
Newton method, optimized anomaly-free method 265—266 282—283
Newton method, optimized minimum-norm method 265—266 282—283
Newton method, positron-helium scattering 292—294
Newton method, positron-hydrogen scattering 285—288
Newton method, principal-value treatment 71—74
Newton method, Schwinger method 265—266
Newton method, Schwinger (iterative) method 269—271
Newton method, Schwinger basis-set method 263—267 276—279
Newton method, separable expansion 69 276—279
Newton method, single-channel study 261—272
Newton method, variational (basis-set) method 69 263—269
Numerical solution of integral equation, atom-diatom (reactive) scattering 300—304
Numerical solution of integral equation, complex Kohn method 267—268 278 301 304
Numerical solution of integral equation, degenerate-kernel scheme 69
Numerical solution of integral equation, electron-atom scattering 294—295
Numerical solution of integral equation, electron-helium scattering 288—292
Numerical solution of integral equation, electron-hydrogen scattering 280—285
Numerical solution of integral equation, electron-molecule scattering 297—300
Numerical solution of integral equation, explicit matrix elements 258—261
Numerical solution of integral equation, four-nucleon scattering 278
Numerical solution of integral equation, inverse Kohn (minimum-norm) method 265—266 282—283
| Numerical solution of integral equation, Kohn (anomaly-free) method 265—266 282—283
Numerical solution of integral equation, Kohn (minimum-norm) method 265—266 282—283
Numerical solution of integral equation, Kohn (off-shell) method 263 265—267
Numerical solution of integral equation, Kohn (on-shell) method 263 281—283
Numerical solution of integral equation, molecular photoionization 296—297
Numerical solution of integral equation, multichannel model 272—275 284—285
Numerical solution of integral equation, neutron-deuteron scattering 278
Numerical solution of integral equation, T matrix (iterative) 269—271 278—279
Pade approximation 69 84 256 279
Partial-wave (expansion), Born phase shift formula 281 291
Partial-wave (expansion), Green’s function 25
Partial-wave (expansion), K matrix 40
Partial-wave (expansion), multichannel 54—56
Partial-wave (expansion), scattering amplitude 18
Partial-wave (expansion), scattering cross section 18
Partial-wave (expansion), t matrix 32—35
Partial-wave (expansion), wave function 15—16 38
Partition 5—6
Photodisintegration of triatomic molecule 240—245
Photoionization 202 210
Photoionization, frozen-core Hartree — Fock method 252—253
Positron-helium scattering 292—294
Positron-helium scattering, close-coupling (CC) method 293
Positron-helium scattering, Kohn method 292
Positron-helium scattering, polarizability 292
Positron-helium scattering, resonance 294
Positron-hydrogen scattering 285—288
Positron-hydrogen scattering, close-coupling (CC) method 286
Positron-hydrogen scattering, complex-energy extrapolation 286
Positron-hydrogen scattering, Harris method 286—287
Positron-hydrogen scattering, Kohn method 285—287
Positron-hydrogen scattering, resonance 288
S matrix 18 31—32 192
S matrix, unitarity 32 57
Scattering, amplitude 14 18 27
Scattering, breakup 3
Scattering, complex potential 85—87
Scattering, cross section 15 18 27
Scattering, distorted wave 193—196
Scattering, eigenphase 57
Scattering, elastic 3
Scattering, electron-atom 255 294—295
Scattering, electron-helium 288—292
Scattering, electron-hydrogen 280—285
Scattering, few-particle 69—70
Scattering, four-nucleon 70 278
Scattering, Green’s function 21—23
Scattering, helium atom 288—294
Scattering, hydrogen atom 279—288
Scattering, inelastic 4
Scattering, length 42
Scattering, multichannel 7 42—60 272—275 284—285
Scattering, nonsingular equation 74—80
Scattering, nucleon-nucleon 255 276—278
Scattering, off-shell 65 159
Scattering, on-shell 65 159
Scattering, phase shift 16—17 34 41
Scattering, positron-hydrogen 285—288
Scattering, potential 3
Scattering, reactive (rearrangement) 3—4 237—240 300—304
Scattering, threshold 4
Scattering, time-independent description 10—13
Scattering, wave-function description 13—27
Scattering, wave-packet description 11
Schwinger method 285—287
Schwinger method, Potential, exponential 261 265 267 269—271
Schwinger method, Reaction cross section 19
Schwinger method, Resonance 36 77 91—96
Schwinger method, Rydberg 261
Schwinger method, Yukawa 261 263 269—271
Separable expansion 257 277—278
Separable expansion, analytic 175
Separable expansion, Bateman 174—175
Separable expansion, energy-dependent 175—176
Separable expansion, Ernst — Shakin — Thaler 175
Separable expansion, Hilbert — Schmidt 173—174
Separable expansion, unitary pole 172—173
Spherical Bessel and Neumann functions 15—16
Spherical Bessel and Neumann functions, half-shell 77—78 159
Spherical Bessel and Neumann functions, hermitian analyticity 30
Spherical Bessel and Neumann functions, post 52—54
Spherical Bessel and Neumann functions, prior 52—54
Spherical Bessel and Neumann functions, t (transition) matrix 18 27
Two-potential formula 196
Unitarity cut 30 35
Variational principle (method), anomalous behavior 215—219
Variational principle (method), anomaly 109 134—136
Variational principle (method), anomaly-free 136—137
Variational principle (method), anomaly-free Kohn 219—222
Variational principle (method), basis-set 108 115—134
Variational principle (method), complex Kohn (rearrangement) 248—249
Variational principle (method), complex Kohn (t matrix) 161—162 186—192 267—268 276—278
Variational principle (method), complex Kohn multichannel 245—249 301 304
Variational principle (method), distorted wave 193—198
Variational principle (method), fractional 160 162 164 165 178
Variational principle (method), general matrix element 201—210
Variational principle (method), Green’s function 188—189
Variational principle (method), Harris 109 128—132 282 286—287 289
Variational principle (method), higher-order 183—186
Variational principle (method), Hulthen 108 112 114 123—124 130—132
Variational principle (method), insertion technique 199—201
Variational principle (method), integral equation 101—107
Variational principle (method), inverse Kohn 108—109 113 121—122 124 130—132
Variational principle (method), iterative scheme 180—182
Variational principle (method), Kato identity 113
Variational principle (method), Kohn 107—122 124 130—132 263 281—283 285—287 292
Variational principle (method), Kohn (anomaly-free) 136—137 265—266 273—275
Variational principle (method), Kohn (K matrix) 106 161—162 186—187 263 265—268
Variational principle (method), least squares 154—157
Variational principle (method), minimum-norm inverse Kohn 132—134 265—266 282—283
Variational principle (method), minimum-norm Kohn 132—134 265—266 273—275 282—283
Variational principle (method), multichannel i?-matrix 145—147
Variational principle (method), multichannel inverse Kohn 143—145
Variational principle (method), multichannel Kohn 137—143 273—275
Variational principle (method), Newton 106 160 176—180 257 267—268 276—278
Variational principle (method), Newton (distorted wave) 197—198
Variational principle (method), Newton basis-set 178—180
Variational principle (method), Newton, iterative 180—182
Variational principle (method), Newton, multichannel inelastic 234—237
Variational principle (method), Newton, multichannel reactive 237—240 300—304
Variational principle (method), Newton, photodisintegration of, triatomic molecule 240—245
Variational principle (method), Newton, with insertion 200—201
Variational principle (method), off-shell 8 159—162
Variational principle (method), on-shell 8 99
Variational principle (method), optimized anomaly-free 148—150 152—154 265—266 282—283 289
Variational principle (method), optimized minimum-norm 148—152 265—266 282—283
Variational principle (method), R matrix 109 124—128 145—147 193 290
Variational principle (method), Rayleigh — Ritz 107 109—111 128—129
Variational principle (method), Rubinow (see “Inverse Kohn”)
Variational principle (method), Schwinger 103 160 162—176 257 262—267 276—278 285—287
Variational principle (method), Schwinger (distorted wave) 197
Variational principle (method), Schwinger (K matrix) 162 164 262—267
Variational principle (method), Schwinger, iterative 180—182 207—208 269—271
Variational principle (method), Schwinger, multichannel 227—234 273—275 284—285
Variational principle (method), Schwinger, with insertion 199—201
Variational principle (method), T matrix 161 210—215
Variational principle (method), trilinear 160
Virtual states 36 96—97
Wave function, incoming-wave 23
Wave function, outgoing-wave 23
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