Examination of the perturbative expansion parameter for piezo-electric coupling in CdS

A perturbative expansion parameter ? is introduced for reformulating the continued-fraction representation of the magneto-optical absorption linewidth function into a power-series expansion. The parameter? is calculated for cadmium sulfide, in which the piezoelectric coupling is dominant, by fitting the theory into the available experiment. The temperature dependence in the quantum limit is shown to be ? T2=1.8, where T is the temperature given in kelvins, or the parameter decreases monotonously as the temperature increases. This is thought to be due to our choice of the continued fraction, which involves the flux variables along with the projectors. We guess that for other piezoelectric materials, the magneto-optical absorption data will have a similar temperature dependence. It is to be regretted that the dependence cannot be checked for the other materials due to lack of experimental data.