Further Contribution to the Theory of the Line-Shape of the Exciton Absorption Band

The line-shape of the exciton absorption band, in the case that k = 0 is at the bottom (or the top) of the exciton energy band and that there are no states with the same energy in order exciton bands, is investigated in the limit of weak exciton-phonon coupling, with the use of the damping theory. The equations for the energy dependent shift and broadening are solved with the aid of graphic calculation. Except for the low temperature region, one can assume the exciton-phonon scattering to be elastic, and the line-shape in the main part of the absorption band is determined essentially by the properties of long wavelength excitons and phonons. The half-value width is rather small, and is proportional to (gT)2 where g is the exciton-phonon coupling constant and T is the absolute temperature. The line-shape is strongly asymmetric, with a tail which is due to the indirect transition, on the high or low energy side according as k = 0 is the bottom or the top of the exciton band.