Isotropic exciton effective mass and scattering by acoustic phonons

2 Isotropic exciton effective mass and scattering by acoustic phonons 

Using the Fermi s golden rule, the probabilities of absorption and emission of a phonon by the exciton system read 

At sufficiently low temperatures, when the thermal energy ksT is much smaller than the exciton bandwidth, most excitons at thermodynamic equilibrium are concentrated in the vicinity of the exciton band minimum in wavevector space. If this minimum corresponds to k = 0 and we assume for simplicity that the excitons have an isotropic effective mass m, we have 

Moreover, under these conditions the relation k a -C 1 (a is the lattice constant) is satisfied for the overhelming majority of excitons. 

The conservation of energy for the absorption and emission processes can now be written as 

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