Preface ....................................................... vii
1 Introduction ................................................. 1
2 Background ................................................... 5
2.1 Symmetry and conservation laws .......................... 5
2.2 Rotational symmetry .................................... 12
2.3 Many-electron atoms .................................... 24
3 Tensor algebra .............................................. 30
3.1 3j symbols ............................................. 30
3.2 Tensor operators ....................................... 38
3.3 Transition matrix elements ............................. 47
3.4 Tensor products ........................................ 51
4 Group theory ................................................ 61
4.1 Cubic crystal field .................................... 61
4.2 Real/tesseral basis .................................... 64
4.3 Octahedral symmetry .................................... 67
4.4 Tensor operators in different groups ................... 70
4.5 Clebsch-Gordan coefficients in different groups ........ 72
5 Many-body effects I: Coulomb interactions ................... 76
5.1 Many-body wave functions ............................... 76
5.2 Many-body matrix elements .............................. 80
5.3 Second quantization .................................... 82
5.4 Two-particle matrix elements ........................... 85
5.5 The Coulomb interaction in momentum space .............. 87
5.6 The Coulomb interaction in spherical symmetry .......... 88
5.7 Coulomb multiplets in lower symmetry ................... 99
6 The scattering amplitude ................................... 104
6.1 The electromagnetic field ............................. 104
6.2 The interaction Hamiltonian ........................... 108
6.3 Multipole expansion ................................... 109
6.4 The scattering amplitude .............................. 112
6.5 Approximate scattering amplitudes and sum rules ....... 118
6.6 Sum rules for a spin-orbit split absorption edge ...... 122
7 Many-body effects II: Solid-state effects .................. 128
7.1 Strongly-correlated materials ......................... 129
7.2 Local potential ....................................... 132
7.3 Effects of neighboring ions ........................... 145
8 X-ray absorption and resonant X-ray scattering ............. 158
8.1 Numerical calculation of X-ray absorption lineshapes .. 158
8.2 The isotropic Ni L-edge X-ray absorption .............. 160
8.3 Trends in isotropic X-ray absorption spectra .......... 171
8.4 X-ray magnetic dichroism .............................. 173
8.5 X-ray linear dichroism ................................ 177
9 Nonresonant and resonant inelastic X-ray scattering ........ 180
9.1 Inelastic X-ray scattering ............................ 180
9.2 Direct resonant inelastic X-ray scattering ............ 187
9.3 Indirect resonant inelastic X-ray scattering .......... 210
Appendix A Tensors ............................................ 225
A.l Spherical basis ....................................... 225
A.2 Tesseral basis ......................................... 226
A.3 Octahedral basis ....................................... 227
References .................................................... 230
Index ......................................................... 233
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