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

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