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| Rodberg L.S., Thaler R.M. — Introduction to the quantum theory of scattering |
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| Предметный указатель |
Phase shift, effective range expansion of 45—52
Phase shift, effective range expansion of, for charged particles 51
Phase shift, effective range expansion of, validity of 49—52
Phase shift, Fredholm expression for see "Fredholm method"
Phase shift, high energy behavior 40 52—63
Phase shift, integral expression for 36—44
Phase shift, low energy behavior 40—52
Phase shift, reality of 33 242 294
Pickup reaction 187 ff. 334—336
Plane wave 30
Plane wave expansion 30 241
Polarization 280 296 299—307
Polarization of incident beam 299 ff.
Polarization of scattered particles 305—307 313—315
Polarization tensor 303
Polarization vector 301—303
Polarization, asymmetry relation 313—316
Positive energy bound states 385
Post-prior paradox 203
Potential matrix see "V Matrix"
Potential operator 172
Potential, complex 326 370
Potential, distorting 321 ff. 330
Potential, final state 333
Potential, Hartree 331
Potential, initial state 333
Potential, local 172
Potential, momentum dependent 371—372
Potential, non-Hermitian 120
Potential, nonlocal 141 173 371
Potential, separable 141—143 153
Potential, spherically symmetric 26
Principal value of integral 98 105
Principal-value integral 107
Probability amplitude 167
Probability conservation 185 226 233 see
Probability current see "Current"
Probability current density see "Current density"
Product space 365
Projection 167
Projection operator 316—320 378 386
Projection operator for angular momentum 318 ff.
Projection operator for spin 317 ff.
Propagation see "Green's function"
Pseudo potential 183 260
Radial Green's function, analiticity property 102
Radial Green's function, boundary conditions 82—83
Radial Green's function, boundary conditions, general 90—93
Radial Green's function, closed form of 79
Radial Green's function, connection between eigenfunction expansion and closed form 87—90
Radial Green's function, definition 79
Radial Green's function, describing point to point propagation 80
Radial Green's function, discontinuity of derivative 82
Radial Green's function, eigenfunction expansions of 84—107
Radial Green's function, general form of 93
Radial Green's function, ingoing-wave 106
Radial Green's function, inhomogeneous part of 98
Radial Green's function, integral equation in terms of 80
Radial Green's function, Mittag — Leffler expansion of 87—90
Radial Green's function, outgoing-wave 96 103
Radial Green's function, outgoing-wave, for unbounded domain 100—107
Radial Green's function, outgoing-wave, in bounded domain 93—95
Radial Green's function, singularity of 90 97 105 107
Radial Green's function, standing wave 86 95 150
Radial Green's function, symmetry of 83
Radial Green's function, unbounded domain 95 ff.
Radial integral equation 289—292 298
Radial wave function see "Wave function"
Radiative capture 340
Raising and lowering operators 262
Reaction matrix see "K Matrix"
Rearrangement collision 187 ff. 197—205 226 324—327 332
Rearrangement collisions 388
Rearrangement collisions, S matrix for see "S Matrix"
Rearrangement cross section see "Cross section"
Reciprocal relation 326 see
Reciprocity 84 117 135—136
Reduced mass 2
Reflection invariance 185 263—266
Refractive index 372
Regularity see "Boundary condition"
Relative coordinate 250 328
Representation of operators 169—171
Representation of vectors 167 ff.
Representative 167
Residual interaction 328 386
Residual potential 78
Resolvent kernel 153
Resonance energy 388
Resonance parameters, relation to interactions 383—389
Resonances 379—389
Retarded Green's function see "Green's function time-dependent"
Reversal of motion 267
Rotation invariance 261—263
Rotation transformation operator 262
Rutherford formula 72
S matrix 34 185 192 224 227—248
S Matrix for ordinary processess 230
S Matrix for rearrangement collisions 230—231
S Matrix, behavior under time reversal 275
S Matrix, diagonalization of 244—248
S Matrix, eigenstates of scattering operator 245
S Matrix, existence of see "Existence of scattering operator"
S Matrix, independent of total momentum 259
S Matrix, paramerization of 277 294
S Matrix, spatial representation of 251
S Matrix, symmetric form of 228—231
S Matrix, symmetry of 277
S matrix, unitarity of 233—234 294
Scalar product 165
Scattered wave 190
Scattering amplitude 7 21 32 292—299
Scattering amplitude, Coulomb 67 69
Scattering amplitude, forward 370 see
Scattering amplitude, integral equation for see "Integral equation"
Scattering amplitude, integral expression for 43 129
Scattering amplitude, nonresonant, elastic 382
Scattering amplitude, partial wave expansion 131
Scattering amplitude, reciprocal relation for 133
Scattering amplitude, reciprocity condition for see "Reciprocity"
Scattering amplitude, spin-dependent 284 295—296 298
Scattering by collection of scatterers 10 361
Scattering by Coulomb potential 63—72
Scattering by hard sphere 36
Scattering by hard sphere, low energy limit 36
Scattering by hard sphere, relation to scattering length 44
Scattering by many-body system 350—363
Scattering by radial delta function potential 80
Scattering by shielded Coulomb potential 68—72
Scattering by square well potential 34—36
Scattering by sum of two potentials see "Two-potential formula"
Scattering experiment, elements of 3—6
Scattering length 44 362 see
| Scattering matrix see "S Matrix"
Scattering of  particle see "Spin one-half"
Scattering operator see "S Matrix"
Scattering state vector see "State vector"
Scattering, cross section see "Cross section"
Schroedinger equation 1 172 328
Schroedinger equation with spin-orbit force see "Spin-orbit force"
Schroedinger equation, integral form of 73—79
Schroedinger equation, justification for use of time-independent 21
Schroedinger equation, operator form of 173
Schroedinger Equation, radial 27 35
Schroedinger equation, regular solution 35
Schroedinger equation, solution of radial equation by means of Green's function 81
Schroedinger equation, time-dependent 17 22 190
Schroedinger equation, time-independent 21 26
Schroedinger picture 212 ff.
Semi classical approximation 61
Shadow scattering 22
Shape dependent parameter 47 49 see
Shape elastic scattering 384
Shielded Coulomb potential see "Scattering by shielded Coulomb potential"
Single scattering approximation 356—359
Source at finite distance 133—135
Source of incident particles 3
Space reflection invariance see "Reflection invariance"
Space translations, invariance under see "Translational invariance"
Spatial representation see "Coordinate representation"
Spherical Bessel functions 28 84
Spherical Bessel functions for large values of argument 29
Spherical Bessel functions for small values of argument 28
Spherical coordinates in 3n dimensions 122
Spherical harmonics 27
Spin 278—320
Spin eigenfunctions 280 286
Spin eigenfunctions, orthogonality of 282
Spin matrix see "Pauli spin matrix"
Spin operators 309—313
Spin projection operator see "Projection operators"
Spin space 308
Spin variable 286 298
Spin, one half 279 ff. 292 314 319
Spin-dependent scattering amplitude see "Scattering amplitude"
Spin-orbit force 272 281
Spin-orbit force, eigenfunctions of 283 ff.
Spin-vector notation 307 ff.
Square well see "Phase shift"
State vector(s) 177—180
State vector(s) in interaction picture 215
State vector(s), antisymmetrization of see "Antisymmetrization"
State vector(s), explicit form 178
State vector(s), final state form of 198—202
State vector(s), ingoing-wave 228
State vector(s), integral equation for 177—180
State vector(s), orthogonality of 178—180
Step function 138
Stripping reaction 334
Symmetry between initial and final states see "T Matrix symmetry
T matrix 34 75 158 182 193 205 247 292—299 see
T Matrix in impulse approximation see "Impulse approximation"
T Matrix on energy shell 161
T Matrix, multiple scattering, expansion for 355 ff. 378
T Matrix, off energy shell 159—162 381
T Matrix, phase relations implied by time reversal invariance 275—276
T Matrix, reciprocal form of 326
T Matrix, symmetry of 202—205 236
T Matrix, unitarity condition 238 240
TARGET 4
Target with spin 297—299
Three-dimensional Green's function see "Green's function"
Time translation operator 212 216
Time translation operator, infinite limit of 217—222
Time translations, invariance under 255
Time-dependent Green's function see "Green's function"
Time-dependent Schroedinger equation see "Schroedinger equation"
Time-dependent treatment of scattering 211—226 see
Time-dependent treatment of scattering, relation to time independent theory 222—225
Time-independent, Schroedinger equation see "Schroedinger equation"
Time-reversal invariance 185 236 266—275 334
Time-reversal transformation operator 268—272
Time-reversed state 268
Time-reversed state, phase of 272—274
Total cross section see "Cross section"
Total momentum see "Momentum"
Transformation operators 165 ff. 252—253 256 262 268
Transformation, generator of 253
Transition amplitude 158 182 see
Transition matrix see "T Matrix"
Transition rate 225
Translational invariance 249—255 332
Translational transformation operator 253
Turning point 52 54
Two-body forces 334
Two-potential formula 40—44 77 80 130—131 148 321—327 373
Two-potential formula for rearrangement collisions 325
Two-potential formula, final state form 326
Two-potential formula, initial state form 326
Two-potential formula, partial wave form of 79
Unit operator 168
Unitarity see "S Matrix"
Unitary operator 171
UNITS 196—197
Unpolarized beam 303
V Matrix 158
Vector addition coefficients see "Clebsch — Gordan coefficients"
Vector space 163 ff. 214 365
Wave function 172 see
Wave function for Coulomb potential see "Coulomb function"
Wave function for motion of center of mass 5
Wave function, asymptotic form 18
Wave function, boundary condition for scattering 6
Wave function, distorted 322 ff. 328
Wave function, expressed as scalar product 168
Wave function, integral equation for see "Integral equation"
Wave function, partial wave expansion 26
Wave function, radial 30
Wave function, radial function 27
Wave function, radial function, asymptotic behavior of 28
Wave function, radial, alternative forms for 75—77
Wave function, radial, normalization of 37
Wave function, solution of integral equation for 132—133
Wave matrix 180 ff. 223 350 354 374
Wave matrix, operator equation for 180
Wave matrix, unitarity of 181—182 223
wave number 124
Wave operator see "Wave matrix"
Wave packet 13—25 189—193 219 227
Wave packet treatment of scattering 13—25
Wave packet, conditions imposed on 17
Wave packet, free particle 14
Wave packet, Gaussian 16
WKB approximation see "JWKB Approximation"
wronskian 53—54 74 83
Zero range approximation 362
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