By accurate calculations of the experimental data of the absorption coefficient, It was found that the obtained optical energy gap of chalcogenide amorphous compositions be produced as a result of direct allowed transition. Is this possible?
Amorphous materials often have a direct or quasi-direct gap. Basically, because states are localised in space, they are delocalised in k-space, so you don't need a phonon to match the momentum of the excited and ground states. Generally, if you want more information on chalcogenide glasses, I recommend the book my Mott & Davis.