R, R' and B Absorption Linewidths and Phonon-Induced Relaxations in Ruby

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Abstract
Widths and shapes of the three groups of absorption lines in ruby are measured in the 77–500°K temperature range. Temperature-dependent linewidths are successfully interpreted in terms of the direct and Raman relaxations. The observed asymmetric shapes of the B 3 and R 3' lines are shown to be due to the energy dependent one-phonon relaxation rate. Non-empirical calculations are made on transition probabilities and stress-induced changes in level splittings of the t 2 3 2 E 1 , 2 T 1 and 2 T 2 states. Orbit-lattice parameters are evaluated using point charge model with Watson's Hartree-Fock function for a free Cr 3+ ion. Mixing of all the doublet states with d 3 electron configuration is taken into account. Agreement between calculation and experiment is surprisingly good. Cubic symmetry approximation and point charge model are shown to be very good. Some slight discrepancies between the calculated rates and experiment are explained by the deviation of the Debye model from a more realistic phonon spectrum deduced from the vibronic structure associated with the R lines.