Resonance Raman scattering induced byFcenters in NaI

Abstract

A systematic study of resonant spectra taken in resonance with the ${\ensuremath{\Gamma}}_{1}^{+}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{4}^{\ensuremath{-}}$ transition ($F$ band) of the $F$ center in NaI is described. Raman-Zeeman experiments allow us to determine the wavelength dependence of the depolarization ratio of the 113-${\mathrm{cm}}^{\ensuremath{-}1}$ resonant mode very accurately in order to test: (i) a semiclassical theory based on the Plazeck's approximation; (ii) a resonant theory which uses a short-time approximation for the propagators of all phonons. It was shown that the semiclassical approach is valid if the energy of the laser line ${E}_{L}$ is lower than 16 500 ${\mathrm{cm}}^{\ensuremath{-}1}$. Within this approximation, standard calculations of spectra (${E}_{L}l16500$ ${\mathrm{cm}}^{\ensuremath{-}1}$) have been done using a linear electron-phonon coupling extended up to the fifth shell of ions surrounding the $F$ center and a softening of the longitudinal interionic force constant between the $F$ center and its first-nearest neighbors (55%) and its first- and fourth-nearest neighbors (23%). The contributions of the ${\ensuremath{\Gamma}}_{1}^{+}$, ${\ensuremath{\Gamma}}_{3}^{+}$, and ${\ensuremath{\Gamma}}_{5}^{+}$ modes to the second moment of the $F$ band deduced from the intensity ratio between the resonant mode and its first overtone are in good agreement with those determined from absorption and magnetic circular dichroism studies. The resonance Raman scattering theory was developed in the case of a spin-orbit interaction in the ${\ensuremath{\Gamma}}_{4}^{\ensuremath{-}}$ excited state stronger than electron-phonon interactions with ${\ensuremath{\Gamma}}_{3}^{+}$ and ${\ensuremath{\Gamma}}_{5}^{+}$ modes. The good agreement between the parameters which fit both the wavelength dependence of the optical absorption line shape ${f}_{{E}_{L}}$ and the Raman intensity justify the short-time approximation used in calculations.