Electric quadrupole interactions in non-axially symmetric electric field gradients of spinI=2 and 3 nuclei in polycrystalline sources

Abstract

Calculations and formulae are presented for the purpose of understanding and analyzing Perturbed Angular Correlation (PAC) experiments that use spin-two and spin-three probe nuclei. For electric quadrupole interactions of probe nuclei in a polycrystalline source with non-axially symmetric electric field gradients, the interaction frequencies and perturbation functions for spin-two and spin-three nuclei differ qualitatively and quantitatively from those for spin-five-halves nuclei. These differences result primarily because them-states of integral-spin nuclei are nondegenerate in an asymmetric electric field gradient. To help the experimenter deal with the added complexity of the integral-spin casesI=2 and 3, closed-form expressions are provided for the energy eigenvalues and the eigenvectors as a function of the asymmetry parameter η. To deal with the problem of calculating the perturbation functionsG _kk (t) for η>0, the summation overm-state quantum numbers is formulated in terms ofa ^(k) _n′,n -coefficients. These coefficients are analogous to theS _kn -coefficients used in the case for η=0. To illustrate the differences between the half-integral-spin caseI=5/2 and the integral-spin casesI=2 and 3, energy difference diagrams anda ⁽²⁾ _n′,n′ diagrams are presented and discussed.