Phonon Self-Energies and $4f$-Electron-Phonon Interaction in ${\mathrm{Ce}}_c{\mathrm{La}}_{1-c}{\mathrm{F}}_3$

In ${\mathrm{Ce}}_c{\mathrm{La}}_{1-c}{\mathrm{F}}_3$ we have observed frequency shifts of optical phonons depending on the concentration $c$ of the $4f$ ions and on temperature. It is shown that these effects are due to a resonant $4f$-electron-phonon interaction via photon-induced virtual quadrupole transitions to excited crystal-field states of ${\mathrm{Ce}}^{3+}$. These shifts are related to the magnetic phonon splitting of doubly degenerate phonons. Both effects can be quantitatively interpreted with the same coupling constant.