Electron-phonon coupling energies from experimental data

For the temperature dependence of the rate of a given multiphonon transition, the least squares fits to the experimental data employing eq. (36.32) are excellent. (See, for example, the suras of squares given in table 36.1.) The comparison of theory and experiment, however, is not clearly satisfactory when the numerical fit involves the multiphonon rates of several rare earth ions in a given crystal, as in the fit of the energy gap dependence. The reason for this difficulty most probably arises from the fact that multiphonon transitions between different electronic levels are coupled to different phonon modes of the crystals, and the concept of a unique fit of effective parameters is, therefore, questionable. Of the effective parameters, L C. deserves further examination. There are rigorous... 

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