Spectral shapes of Mössbauer absorption and incoherent neutron scattering from harmonically bound nuclei in Brownian motion: Applications to macromolecular systems

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Abstract
The Mössbauer resonance absorption line in solids is of narrow, natural width. In viscous liquids the linewidth is broadened by diffusion. In many biological systems—whole cells, membranes, or proteins—at temperatures above the freezing point of the internal water, a superposition of broad and narrow lines is observed. Here, the Mössbauer spectral shapes expected in this new ‘‘phase’’ of proteinic matter are calculated. The calculation is based on the assumption that the unfrozen conformational degrees of freedom of the macromolecules can be described in terms of damped harmonic oscillators acted upon by random forces. The known classical correlation functions for harmonically bound particles in Brownian motion are utilized to calculate the Mössbauer spectra. The theory predicts the following: a spectrum which can be approximated by a superposition of a narrow and a broad line; and a sharp decrease in the total resonance absorption as a function of temperature and asymmetric quadrupole doublets in Fe57 spectra, even when the Debye-Waller factor is isotropic but the damping frequencies are anisotropic. The presented formulas, with only minor changes, are also applicable to the description of neutron quasielastic scattering from systems in which nuclei diffuse in restricted geometries: bound diffusion on surfaces, lamellar systems, ionic polymers, biopolymers, and membranes. Finally, calculated spectra are compared to recent experimental Mössbauer spectra, and the agreement is outstanding. The spectral shape of particles participating in both bound translational and free rotational diffusion is also calculated.