Analysis of Raman Scattering byFCenters

First-order Raman scattering has recently been measured by Worlock and Porto in NaCl and KCl colored with $F$ centers. We carry out a quantum-mechanical calculation of the Raman cross section which shows that the frequency spectrum of phonons measured by Raman scattering is the same as the frequency spectrum of the phonons that broaden the $F$ band. A lattice mode contributes to the Raman cross section in proportion to its contribution to the second moment of the $F$ band. Our calculated value for the cross section, 2.0×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, is in reasonable agreement with the measured value of the cross section, ≈5×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$. The spin-orbit coupling in the first excited state of the $F$ center, which also contributes to the broadening of the $F$ band, causes Raman scattering in which there is a spin transition of the $F$ center.