Effect of Molecular Shape and Flexibility on Gamma-Ray Directional Correlations

Abstract

The perturbed angular correlation for a gamma-ray cascade from a nucleus rigidly bound to an asymmetric-top molecule in solution has been calculated, using a diffusional model for rotational reorientation. When molecular rotation is rapid [all diffusion constants Di ≫ (1/6τn), where τn is the lifetime of the intermediate nuclear state of the cascade], a treatment analogous to that in nuclear magnetic resonance leads immediately to the desired attenuation factor. On the other hand, when molecular rotation is slow [all Di≪ (ω 0/6), where ω0 is the fundamental quadrupole frequency], the derived form of the angular correlation may not contain a separable attenuation factor. These calculations are illustrated by several plots of the integral anisotropy for symmetric-top molecules of fixed shape and varying size, for several choices of the characteristic ``angle of attachment'' between the molecular symmetry axis and the principal axis of the electric field gradient at the nucleus. Finally, it is shown that the case of a tracer bound through a single flexible link to a spherical molecule is formally identical to the case of a tracer rigidly bound to a symmetric-top molecule; the resultant integral anisotropy is plotted for several fixed rates of internal rotation in spherical molecules of varying size, for several choices of the ``angle of attachment'' between the electric field gradient and the axis about which internal rotation occurs. The conclusions of practical significance are (1) the perturbed angular correlation depends only weakly on the shape of the molecule, while (2) in contrast, the correlation can be markedly affected by the presence of even relatively slow internal rotation at the site of attachment of the tracer to the molecule.