Abstract
Starting with the Kubo formalism and using the projection operator technique (POT) introduced by Kawabata, the optical quantum transition line-profiles (QTLPs) formula for a Mn-doped wurtzite GaN film was derived as a function of temperature at a frequency of 9.49 GHz (X-band), on the basis of continued fraction representation (CFR) which is a counterpart of the conventional series expansion (CSE). Utilizing this formula we obtained the fine-structure parameter a - F = 9.4 ×10-4 cm-1 and fitting parameter ζ= 4.1. The optical quantum transition half-widths (QTHWs) obtained with the use of these parameters agrees quite well with the existing experimental result in the temperature region T > 20 K. The QTHWs increase with increasing temperature due to the interaction of electrons with optical phonons. Thus, the present technique is considered to be more convenient to explain the resonant system as in the case of other optical transition problems.
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