Jahn-Teller effect on ${\mathrm{PrO}}_2:$ A multimode vibronic model

Recent well resolved neutron spectroscopy measurements of the magnetic excitations in ${\mathrm{PrO}}_2$ provide evidence of the dynamical Jahn-Teller effect on this dioxide. We calculate the differential cross section in a wide range of energy and the magnetic moment of ${\mathrm{PrO}}_2$ after the analysis of different vibronic models (one-mode and two-mode phonon coupling models) for electrons interacting with distortions of e and $t_2$ symmetry. The Lanczos-recursion procedure is followed to determine the vibronic states in a nonperturbative way and with high precision. A very convenient choice of the initial state of the Lanczos chain is suggested here so allowing easy calculation of the differential cross section. It is found that e modes do not give reliable results in terms of intensities of the expected transitions, while $t_2$ modes in a multimode vibronic model lead to a quite good agreement with the experimental measurements.