4 X-ray Dichroisms in Spherical Tensor and Green’s Function Formalism
121
Fig. 4.14 Fundamental spectra for a quadrupole transition in a 3d 9 ion in an octahedral crystal
field. Re and Im are the real and imaginary parts of the spectra
have k [
1
√
2
1
√
2
0] and is rotated about the [
1
√
2
1
√
2
0] axis as depicted in Fig. 4.16b.
The XAS cross section shows a clear twofold angular dependence in these settings.
It is interesting to discuss the difference between both scattering geometries and
the reason behind the absence of angular dependence in the first case. In Fig. 4.15,
we plot the angular dependence of the light tensor [E(4, 0), E(4, 4), and E(4, −4)]
for both cases. The contribution of the term E(4, 0) is 90
◦ out-of-phase with respect
to the terms E(4, 4) and E(4, −4) for the first scattering geometry [see panel (a)
of Fig. 4.15]. The O h symmetry implies that the ratio between the R(4, 0) and the