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Abstract
The diagram approach is used to determine the locations of the singularities of the monomer self energy in isotopic mixed molecular crystals. The cumulant functions, which are the relative weights of the diagrams in the series, are evaluated in a self consistent manner. The resulting self energy expression is seen to contain singularities which are dependent on the concentration of guest molecules in the system. The formalism is used to obtain the locations of the singularities as a function of the reciprocal trap depth for different concentrations of naphthalene-h 8 in a host naphthalene-d 8 crystal.