Theory of Molecular Rydberg States

Cover
......Page 1
THEORY OF MOLECULAR RYDBERG STATES......Page 3
Cambridge Molecular Science......Page 5
Title
......Page 7
Copyright
......Page 8
Contents......Page 9
Preface......Page 13
1.1 The nature of Rydberg states......Page 15
1.2 Organization of the text......Page 21
References......Page 29
2.1 Introduction......Page 31
2.2 Coulomb wavefunctions......Page 32
2.2.1 Closed-channel solutions: E <  I......Page 35
2.2.2 Strongly closed channels......Page 36
2.3 Single-channel quantization......Page 39
2.4 Coupled channels......Page 41
2.4.2 Resonant case......Page 44
2.4.3 Closed-channel case......Page 51
3.1 Traditional quantum chemistry......Page 59
3.2 Constrained ab-initio wavefunctions......Page 66
3.3 The R-matrix matching procedure......Page 68
3.4.1 R-matrix derivation......Page 72
3.4.2 Buttle correction......Page 74
3.5.1 Standard method......Page 76
3.5.2 Eigenchannel method......Page 80
3.5.3 Convergence tests......Page 84
3.5.4 Spheroidal basis functions......Page 87
3.6 Rydberg-valence interactions......Page 88
3.7.1 General considerations......Page 92
3.7.2 Group II mono-fluorides......Page 96
3.7.3 Dipole modified Coulomb functions......Page 99
4 Frame transformations and channel interactions......Page 104
4.1.1 The classical picture......Page 105
4.1.2 Frame transformation types......Page 110
4.2.1 Elementary case (b) → case (d) transformation......Page 111
4.2.2 Λ-doubling......Page 114
4.2.3 l-uncoupling in non-penetrating series......Page 115
4.2.4 Stroboscopic beats between electronic and nuclear motion......Page 117
4.3 Vibrational channel interactions......Page 119
4.3.1 Bound-state eigenvalues......Page 121
4.3.2 Vibrationally induced auto-ionization and rotational branching ratios......Page 123
4.4.1 Configuration interaction......Page 128
4.4.2 Jahn–Teller channel coupling......Page 129
5 Competitive fragmentation......Page 139
5.1 Perturbation model for diatomic species......Page 140
5.2 Diatomic predissociation......Page 143
5.3.1 Competing processes......Page 144
5.3.2 Two-step theory......Page 149
5.4 R-matrix formulation......Page 154
5.5.1 The Jahn-Teller mechanism......Page 162
5.5.2 A spectroscopic related model......Page 167
6.1 Introduction......Page 171
6.2 n-photon discrete absorption......Page 172
6.2.1 Single-photon absorption......Page 173
6.2.2 Coherent two-photon absorption......Page 174
6.3 Spherical tensor representation......Page 177
6.4 Spatial selectivity......Page 181
6.5 Resonant two-photon excitation......Page 184
6.6 Multiphoton band structure......Page 185
6.6.1 Symmetric tops......Page 186
6.6.2 Asymmetric tops......Page 188
6.7 Angular momentum decoupling in high Rydberg states......Page 191
6.8 ZEKE intensities......Page 197
6.8.1 Asymmetric band profiles......Page 198
6.8.2 Symmetry selection rules......Page 201
7 Photo-ionization......Page 205
7.1 Boundary conditions and cross-sections......Page 206
7.2 The photo-ionization matrix element......Page 209
7.3.1 General formulation......Page 213
7.3.2 Photo-ionization selection rules......Page 214
7.4.1 General formulation......Page 216
7.4.2 Asymmetry parameters......Page 220
7.4.3 Information content......Page 227
7.5 Fixed molecule angular distribution......Page 229
7.6.1 The optical density matrix......Page 233
7.6.2 1+1\' REMPI photo-electron angular distribution of NO......Page 237
7.7.1 General formulation......Page 240
7.7.2 Experimental determination......Page 245
7.8 Spin polarization......Page 246
8.1 Rydberg wavepackets......Page 253
8.1.1 Recurrence and revival......Page 254
8.1.2 Coherent control......Page 263
8.1.3 Time-dependent photo-fragmentation......Page 266
8.2.1 Symmetry considerations......Page 269
8.2.2 Parabolic states of the H atom......Page 272
8.2.3 Stark states of the H atom......Page 274
8.2.4 Non-hydrogenic species......Page 279
8.2.5 Generalized MQDT theory......Page 281
References......Page 285
A.1 Open channels......Page 287
A.2 Closed channels......Page 289
B.1 Standard representation......Page 292
B.2 Sine-cos representation......Page 293
B.3 Mixed representation......Page 294
C.1 Hund\'s cases for diatomic molecules......Page 296
C.2 Parity considerations......Page 298
C.3 Basis functions......Page 299
C.4.1 Case (b) to case (d) frame transformation......Page 300
C.4.2 Case (a) to case (e) frame transformation......Page 302
C.5.1 Symmetry considerations......Page 304
C.5.2 The case (b) to case (d) frame transformation......Page 307
D.1 Discrete absorption amplitudes......Page 309
D.2.1 Multichannel boundary conditions......Page 311
D.2.2 Photo-ionization matrix elements......Page 313
D.3 Dipole radial matrix elements and Cooper minima......Page 317
 Appendix E: Generalized MQDT representation......Page 321
F.2 Reduced matrix elements......Page 324
References......Page 326
Index......Page 328