Jahn-Teller Effect in the ${}_{}{}^4{}_{}{}^{}T_{1g}^{}{}_{}{}^{}\mathrm{}\left(I\right)\mathrm{}$ State of ${\mathrm{Mn}}^{++}$ in RbMn${\mathrm{F}}_3$. II

A quantitative treatment of the experimental results of the preceding paper is presented. Taking account of spin reorientation under stress, the Ham reduction factor could be calculated in three different ways. These lead to a value $E_{\mathrm{JT}}\cong 760$ ${\mathrm{cm}}^{-1\mathrm{}}$. Using approximate force constants for the Mn-F relative displacement and the [100]-stress response, a value of $E_{\mathrm{JT}}\cong 730$ ${\mathrm{cm}}^{-1\mathrm{}}$ was obtained. From the isotropic-stress response a value for the symmetric displacement was found, and when this is added to the $E_g$ displacement, the equilibrium bond lengths in the excited state are obtained. By making a Fourier analysis of the displacement in terms of the vibrational modes of the crystal, Franck-Condon factors were found and the spectrum of the phonon sidebands was calculated. This agreed well with the observed spectrum. The phonon sideband is further used to confirm the absence of a $T_{2g}$-type distortion.