Theory of two-exciton absorption of light with allowance for lattice vibrations

A study is made of the two-exciton absorption of light in molecular crystals at nonzero temperatures. A unitary transformation is proposed that enables one to diagonalize partly the energy operator of the crystal and investigate directly the cases of both strong and weak exciton-phonon coupling. For the case of strong coupling, the temperature dependences of the line intensity for double absorption and the energy distance between lines of a permutational doublet are obtained. Allowance for the exciton-phonon interaction also leads to the possible appearance of new lines. Formulas are obtained for the coefficient of absorption of light by a crystal in the frequency range corresponding to the excitation of two Frenkel excitons and phonons.