When we are in the case of an indirect optical transition assisted by more than one phonon (2 or more), how should we proceed for determining the indirect gap and the energy of each phonon.
If you know the energy of the absorbed photon, and the energy of some/all of the radiated photons, then perhaps the phonon energies could be found from the difference of the two?
Like if you know you absorbed two 514 nm photons and emitted one 800 nm photon (as a wild example) then your phonon energies must correspond to ~ (2*514 - 800) = 228 nm?
Can you post a diagram of the transitions you are looking at?
This energy sounds unusually large, especially considering 0.025 eV thermal energy to play with at room temperature. Even if a transition like this could theoretically exist, it would be difficult to get in practice. What are you using to make your measurement and at what temperature is the measurement performed? Do you know the Debye temperature of your material?