Slow motion lineshapes

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Abstract
A slow motion expansion about the characteristic features of the powder spectrum is presented. Analytic expressions for the lineshape function, modulated by slow rotational diffusion, are derived. It is shown that the slow motion limit is characterized by harmonic oscillator equations of motion, and the resulting spectrum is determined by harmonic oscillator eigenvalues. The essential features of the lineshape show up naturally, and in particular the axial lineshape diverges like τ1/4 while there is only a weak motional correction to the logarithmic divergence of the non-axial lineshape. The dynamic frequency shifts converge to their static limits like τ-1/2 for all cases.

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