Symmetry property of the electric quadrupole perturbation function in gamma ray angular correlations

The experimental measurement of the perturbed angular correlation (PAC) of radiation emitted from probe nuclei implanted in a host lattice is becoming an increasingly important analytical technique. Most recent measurements have involved single crystal samples which are more informative than polycrystal ones, and the perturbing fields have not necessarily been axially symmetric. In these cases the theoretical treatment of the data is necessarily more complex. We have investigated the perturbation function applicable in the case of the hyperfine interaction of probe ions implanted in a host matrix. It is shown that in the general case of y-y correlations involving static electric quadrupole interactions the Perturbation function can always be expressed as a sum of cosine terms, without having to make any assumption about the axial symmetry of the perturbing field or employing the averaging procedure used in the case of polycrystalline hosts. Though many have used this fact, the formal justification for it in this most general case has not been presented before.