How can f-f transitions happen?
So I am currently reading the book: Physical Inorganic Chemistry A Coordination Chemistry Approach, S. F. A. Kettle

One of the chapters deals with Lanthanides and Actinides and their spectra. After a long introduction on different energetic levels and spin-orbit coupling there are a few remarks on $\ce{f-&gt;f}$ transitions although, as the author chooses to explain different ideas and phenomena during his explanation I am not sure if I fully understood his final conclusion. I guess it's probably a sum of many contributions. To summarize it quickly the aspects he is discussing are:


We can see that the intensities for $\ce{f-&gt;f}$ transitions in coordination polyhedra with high symmetry tend to be weaker than in low symmetries. That means that there are probably mechanisms such as vibrations and mixing with other orbitals, presumably d-orbitals (like in $\ce{d-&gt;d}$ transitions).
For the vibronic coupling (in order to compensate for a parity forbidden transition) he gives $\ce{NaCs2[YCl6]:M^3+}$ as an example, where at low temperatures both electronic and vibrational transitions seem to be observable for the trivalent lanthanide dopant.
Then there are also 'bands' under high-resolution conditions that cannot be explained by vibronic coupling. This is where he introduces magnetic dipole allowed transitions. In his explanation he compares how an electric dipole will invert at an inversion center while, much like in the detectors for mass spectrometers, electrons will be forced to move in a spiral along the magnetic vector and a spiral or circle does not invert here. According to his explanation the magnetic dipole is an even function and as f-orbitals are odd an $\ce{f-&gt;f}$ transition is $$u * u = g$$
and therefore magnetic dipole allowed. 
Then he also refers to the fact that even though light may not be absorbed in matter it will still travel slower through a medium than through vacuum since it causes oscillations that have to propargate through the medium first.
I'll just quote the book at this part:



  It has been suggested that the light wave used in absorption studies
  polarizes the ligands and that the lanthanide ion feels the dipoles created.
  That is, it is suggested that the ligands provide a non-centric field at the
  lanthanide ion not by virtue of any vibrational movement of their nuclei but
  because of the instantaneous polarization of their electron density caused by
  the light wave itself.



Then there was a remark on the environment as well. Since the f-orbitals don't really take place in any bonding for the lanthanides, do they actually feel their environment? And for this they considered weak nephelauxetic effects. 
And then there are so called hypersentisitve-transitions (transitions with environment sensitive intensities). And those seem to be related to quadrupole-allowed transitions. The two dipoles in a quadrupole may arise from a polarization by the electric vector as mentioned above. So one dipole is the light vector itself (with the energy corresponding to the hypersentisitve-transitions and the other one being the induced dipole).
The difference in environments would arise from different polarizabilities of the ligands in different environments.

The other mechanism seems a bit more complicated. It considers low-symmetry crystal fields with an inherent dipole. So high-symmetry crystal fields distort via a vibration to a low symmetry. The ligand environment is distorted to a point where it become dipolar.
And then the light itself is the other dipole. 
The final remark was on the bonding in f-orbitals. Here the complex $\ce{[UF8]^3-}$ was considered. By repulsion a square antiprism would be favored if there was no interaction at all with the ligands. What we find however is a cubic arrangemenent. 
And the $\ce{f_{xyz}}$ orbital can contribute to a bond only in the cubic case.