Abstract
In thin crystals the damping of a molecular exciton which interacts with Einstein phonons and randomly distributed impurities is calculated by means of Green's functions. The finite sample size is taken into account by constructing a Green's function which vanishes at the sample boundary. The damping shows an oscillatory behavior due to the small thickness of the molecular crystal. The order of magnitude of the damping is in agreement with Brodin's experiments on thin anthracene crystals at 20\ifmmode^\circ\else\textdegree\fi{}K. It is demonstrated that extremely purified naphthalene crystals should also show an oscillatory dependence of the absorption coefficient on the thickness of the crystal.
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