  Temperature-dependent radiative recombination of free excitons involving one
or two LO phonons in GaN is investigated in detail. It is found that both
phonon sidebands possess asymmetric lineshape and their energy spacings from
the zero phonon line strongly deviate from the characteristic energy of LO
phonons as the temperature increases. Furthermore, the deviation rates of one
and two phonon sidebands are significantly different. Segall-Mahan theory,
taking the exciton-photon and exciton-phonon interactions into account, is
employed to calculate the sidebands of one or two LO phonons for free excitons
in a wide temperature range. Excellent agreement between theory and experiment
is achieved by using only one adjustable parameter (effective mass of free
excitons). The obtained effective mass indicates that the free excitons in GaN
are likely much lighter than estimated by available theoretical studies.
