Mutual influence of energy transfer and lattice phonons

The theory of the energy-transfer process in a crystal lattice is revised. At low temperatures and at small energy differences between excited levels of donors and acceptors the conventional assumption about equilibrium lattice phonons is no longer valid. Above a certain characteristic excitation concentration, it is necessary to take into account the time dependence of phonon populations. A coupled system of equations for the mean electronic and phonon populations is derived. Two situations of phonon-assisted energy transfer in crystal lattice are analyzed: (a) energy transfer between impurities with inhomogeneously broadened energy levels; (b) the transition of a free exciton from an exciton band to a local level. For these specific cases the characteristic concentration is found. Concrete experimental situations where stimulated emission of phonons may be observed are suggested [doped molecular crystal and optically active impurity doped ruby (${\mathrm{Al}}_2$${\mathrm{O}}_3$:${\mathrm{Cr}}^{3+}$) crystal system].