Perturbed Directional Correlation in Tantalum-181

Abstract

The effect of a static quadrupole interaction on the 133-482-keV gamma-gamma angular correlation in ${\mathrm{Ta}}^{181}$ has been studies by the delayed-coincidence method. Using a source of ${\mathrm{Hf}}^{181}$ in polycrystalline hafnium metal, the anisotropy was measured as a function of the time between the formation and decay of the 482-keV state with a fast-slow coincidence spectrometer. The anisotropy as a function of time clearly revealed fluctuations arising from the reorientation of the nuclear spin due to coupling of the quadrupole moment of the 482-keV state with the electric-field gradients of the crystals. The interaction strength evaluated on the basis of the theory for axially symmetric gradients was ${\ensuremath{\omega}}_{0}=299\ifmmode\pm\else\textpm\fi{}8$ Mc/sec. Evidence for the presence of a rhombic (nonaxially-symmetric) electric interaction was observed in the departure of the results from the predictions for the axially symmetric case. The results are, however, in agreement with the theory for rhombic interactions if the electric field gradient in the hafnium crystals is assumed to have an asymmetry parameter $\ensuremath{\eta}=0.30\ifmmode\pm\else\textpm\fi{}0.03$, and in addition, if a normal frequency distribution of full width at half-maximum equal to 10% is used to describe the variation of the field gradient from site to site. Further, using the evidence from Coulomb excitation for the strong deformation of the tantalum nucleus, we determined the quadrupole moment of the 482-keV state to be $Q=(2.53\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$. This allows the calculation of the field-gradient magnitudes in metallic hafnium, which yields ${V}_{\mathrm{zz}}=\ifmmode\pm\else\textpm\fi{}(5.18\ifmmode\pm\else\textpm\fi{}0.27)\ifmmode\times\else\texttimes\fi{}{10}^{17}$ V/${\mathrm{cm}}^{2}$, ${V}_{\mathrm{yy}}=\ensuremath{\mp}(3.37\ifmmode\pm\else\textpm\fi{}0.19)\ifmmode\times\else\texttimes\fi{}{10}^{17}$ V/${\mathrm{cm}}^{2}$, and ${V}_{\mathrm{xx}}=\ensuremath{\mp}(1.81\ifmmode\pm\else\textpm\fi{}0.25)\ifmmode\times\else\texttimes\fi{}{10}^{17}$ V/${\mathrm{cm}}^{2}$. Incidentally, the half-life of the the 482-keV state was remeasured to be 10.4\ifmmode\pm\else\textpm\fi{}0.2 nsec, consistent with prior determinations.