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In synchrotron Moessbauer spectroscopy, the nuclear exciton polaritonmanifests itself in the lineshape of the spectra of nuclear forward scattering(NFS) Fourier-transformed from time domain to frequency domain. This lineshapeis generally described by the convolution of two intensity factors. One of themis Lorentzian related to free decay. We derived the expressions for the secondfactor related to Frenkel exciton polariton effects at propagation ofsynchrotron radiation in Moessbauer media. Parameters of this Frenkelian shapedepend on the spatial configuration of Moessbauer media. In a layer of uniformthickness, this factor is found to be a simple hypergeometric function. Next,we consider the particles spread over a 2D surface or diluted in non-Moessbauermedia to exclude an overlap of ray shadows by different particles. Deconvolvingthe purely polaritonic component of linewidths is suggested as a simpleprocedure sharpening the experimental NFS spectra in frequency domain. Thelineshapes in these sharpened spectra are theoretically expressed via theparameters of the particle size distributions (PSD). Then, these parameters aredetermined through least-squares fitting of the line shapes.

Nuclear forward scattering in particulate matter: dependence of lineshape on particle size distribution