Spectra and mobility of self-trapped ST excitons

The function n(R) in (3.160) represents the wavefunction of a harmonic oscillator with the normal coordinate qK qK aa is its equilibrium position corresponding to such a crystal state, when one molecule na is excited, and the quantum number Nk = 0,1, 2. indicates the state of the oscillator k. 

The quantities E a 0 in (3.161), due to the translational symmetry, do not depend on the vector n. In crystals where their symmetry operations contain an element which transforms the molecules of a unit cell into each other, the quantities E a 0 also do not depend on the index a. The wavefunction in the considered simple factorized approximation has the form 

The states (3.162) were obtained under the assumption that the resonant inter-molecular interaction is small. Here we notice that attempts to improve the above method of computation of crystal states in the case of a strong exciton-phonon interaction has been made in a series of works (see (23)-(25)). 

In particular, Rashba (23) has considered such crystal excited states, where the excitation is not centered at one molecule, as was assumed in (3.162), but is smeared out about a certain finite crystal region. In this case, when the time of the resonant excitation transfer from one molecule to another is small compared to the time needed by the molecule to achieve a new equilibrium position21 a local deformation can occur within some excitation region similar behavior is observed in the case of polarons (20). The shape of the deformation is consistent with the shape of the excitation distribution inside the same crystal region. If, in particular, the resonant interaction tends to zero, the states, obtained in Ref. (23), are identical with that given by formula (3.162). 

Finally we remark that within the same excitonic band, if its width is sufficiently large, one can find both states, for which the exciton-phonon interaction is strong, and states where it is weak so that these states can be computed by means of perturbation theory (for a more detailed discussion of this problem see Ref. (18)). Only in the limit of very narrow excitonic bands do the excitonic states show the character of localized excitons, on which we have concentrated our attention. In all references which we have mentioned above the variational method was used, which gives only the lowest states in the excitonic band. 

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