Temperature Dependence of Exciton Absorption Spectra. A Calculation Based on the Recursion Method

Based on the recursion method of calculating correlation functions, the absorption spectra of a model of a three‐dimensional dielectric crystal containing a band of Frenkel excitons interacting with a branch of dispersionless optical phonons, are investigated in a wide range of material parameters and temperatures. The cases of a weak exciton—phonon coupling, vibronic exciton, coexistence of nearly free and self‐trapped excitons as well as intermediate situations are considered. It is shown that in a definite region of parameters the character of exciton—phonon coupling is changed with the growth of temperature so that the weak‐coupling‐type spectrum acquires some features of the vibronic exciton spectrum. In addition, in a definite temperature range, a change in the physical meaning of the observed peculiarities occurs. In the case of the coexistence of nearly free and self‐trapped states the temperature behaviour of the related peculiarities are shown to be different, a fine structure caused by self‐trapped states is manifested in the vicinity of the main peak only in the low‐temperature spectra. At higher temperatures the spectral shape can essentially differ from the asymmetric Lorentzian due to a sideband in a short‐wave side of a maximum. A long‐wave absorption tail at high temperatures and the considered sets of parameters satisfies the Urbach rule. With the lowering of temperature in the case of weak coupling a structure with a step approximately equal to the phonon frequency stands out in this tail.