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We consider the Jahn-Teller system E\ensuremath{\bigotimes}\ensuremath{\epsilon} consisting of an orbital doublet coupled with a two-dimensional phonon. We attack the problem within the continued-fraction formalism, and we provide exact solutions for the optical absorption, the magnetic circular dichroism, and the reduction factors of the electronic orbital angular momentum. The elegant solutions provided by the continued-fraction formalism allow us to study the system in any range of coupling, where other methods in the literature would be inadequate. In particular, Slonczewsky resonances are clearly established in the strong-coupling case.

We have theoretically analyzed the Jahn-Teller effect in the near-infrared absorption spectrum of ${\mathrm{Fe}}^{2+}$ ions in CdTe. We have assumed a linear active interaction on the $^{5}\mathrm{T}_{2}$ levels of the 3${d}^{6}$ electrons of the ${\mathrm{Fe}}^{2+}$ impurity; the phonon symmetry taken into account is ${\ensuremath{\Gamma}}_{3}$. The spin-orbit interaction has also been included. By means of the recursion method and an appropriate choice of the dipole-carrying initial state, we have calculated in a nonperturbative way the absorption spectrum of ${\mathrm{Fe}}^{2+}$ ions in CdTe, including a large number of phonons. The theoretical absorption spectrum and some temperature-dependent features are discussed and compared with the available experimental data.

The vibronic model for ${\mathrm{Fe}}^{2+}$ impurities in zinc sulfide crystals is analyzed theoretically with the recursion method. It is shown that the far-infrared absorption spectrum of iron ions can be understood by taking into account the coupling of the electronic state $^{5}\mathrm{T}_{2}$ to phonons of symmetry ${\ensuremath{\Gamma}}_{3}$ in three different energy ranges: a low-energy phonon of frequency \ensuremath{\Elzxh}${\ensuremath{\omega}}_{1}$\ensuremath{\approxeq}25 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, an intermediate-energy one of frequency \ensuremath{\Elzxh}${\ensuremath{\omega}}_{2}$\ensuremath{\approxeq}125 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and a high-energy one of frequency \ensuremath{\Elzxh}${\ensuremath{\omega}}_{3}$\ensuremath{\approxeq}300 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The corresponding Jahn-Teller energies are estimated as ${E}_{\mathrm{JT}1\mathrm{\ensuremath{\approxeq}}50}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, ${E}_{\mathrm{JT}2\mathrm{\ensuremath{\approxeq}}130}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and ${E}_{\mathrm{JT}3\mathrm{\ensuremath{\approxeq}}70}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Theoretical predictions of the vibronic multimode model for the infrared-absorption spectrum are compared with experimental results and previous speculations available in the literature.