Interactions between frenkel excitons. I. Formalism and preliminary results

For the tightest-bound Frenkel excitons a many-particle hamiltonian is adopted which includes terms representing interactions between the excitons. The parameters of the model are the excitation energy of an isolated localized excitation, the excitation-transfer matrix elements, and the interaction energies. Several special cases, involving particular relations between the latter two sets of parameters, are treated qualitatively. Equations are translated into the language of spin-$\text{1}\text{2}$ lattices, so that use may be made of the results of that theory. Favorable conditions for observation of polyexcitons and of phase transition to a liquid of excitons are discussed. A standard formalism for the determination of absorption and emission spectra and of their moments is adapted to the present problem. Possible generalizations of the model are briefly discussed.