Abstract
AbstractSeveral different properties of a fractal are calculated: the recoilless fraction, the Raman scattering intensity, and the spin–lattice relaxation time. The recoilless fraction of a Mössbauer nucleus in a fractal is calculated from the displacement of an atom in a fractal which exhibits a scale invarince for a noninteger fracton dimensionality and found to be in good agreement with the measurements in deoxygenated myoglobin. The exponent of the normalized intensity of the Raman scattered light with frequency is calculated using fractional dimensionalities and density of states for decaying as well as nondecaying fractons. It is found that the phonon and the fracton branches may crossover or avoid crossing giving rise to new modes called as fracnons. The calculated Raman intensity is in good agreement with the measurements in silica gel, (C2H5O)4Si. A theory of the spin–lattice relaxation with the dimensionality crossover is presented. The calculated value of the spin–lattice relaxation time is found to be in good agreement with the measured value of Fe3+ in a frozen solution of metmyoglobin azide.
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