Nuclear Matrix Elements in the First-Forbidden Beta Decay of the Eu 152 Ground State

The degree of circular polarization ${P}_{c}({\ensuremath{\theta}}_{\ensuremath{\beta}\ensuremath{\gamma}})$ and the directional correlation $W({\ensuremath{\theta}}_{\ensuremath{\beta}\ensuremath{\gamma}})=1+{A}_{2}(W){P}_{2}({cos\ensuremath{\theta}}_{\ensuremath{\beta}\ensuremath{\gamma}})$ were measured in the ${3}^{\ensuremath{-}}(1.49\ensuremath{-}\mathrm{M}\mathrm{e}\mathrm{V} {\ensuremath{\beta}}^{\ensuremath{-}})\ensuremath{\rightarrow}{2}^{+}(0.344\ensuremath{-}\mathrm{M}\mathrm{e}\mathrm{V} \ensuremath{\gamma})\ensuremath{\rightarrow}{0}^{+}\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ cascade leading from the ground state of ${\mathrm{Eu}}^{152}$ to the ${\mathrm{Sm}}^{152}$ ground state. The angle ${\ensuremath{\theta}}_{\ensuremath{\beta}\ensuremath{\gamma}}$ is the angle between the $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ momentum vectors. Representative values of ${P}_{c}({\ensuremath{\theta}}_{\ensuremath{\beta}\ensuremath{\gamma}})$ measured at $\overline{W}=3.20$ (in units ${\mathit{mc}}^{2}$) for some average angles ${\overline{\ensuremath{\theta}}}_{\ensuremath{\beta}\ensuremath{\gamma}}$ are: ${P}_{c}(90\ifmmode^\circ\else\textdegree\fi{})=\ensuremath{-}0.01\ifmmode\pm\else\textpm\fi{}0.09$, ${P}_{c}(130\ifmmode^\circ\else\textdegree\fi{})=+0.33\ifmmode\pm\else\textpm\fi{}0.07$, ${P}_{c}(157\ifmmode^\circ\else\textdegree\fi{})=0.33\ifmmode\pm\else\textpm\fi{}0.07$, ${P}_{c}(171\ifmmode^\circ\else\textdegree\fi{})=0.24\ifmmode\pm\else\textpm\fi{}0.10$. Some representative values of the directional correlation coefficient ${A}_{2}(W)$ are: ${A}_{2}(2.8)=\ensuremath{-}0.335\ifmmode\pm\else\textpm\fi{}0.006$, ${A}_{2}(3.15)=\ensuremath{-}0.363\ifmmode\pm\else\textpm\fi{}0.006$, ${A}_{2}(3.4)=\ensuremath{-}0.381\ifmmode\pm\else\textpm\fi{}0.005$, ${A}_{2}(3.7)=\ensuremath{-}0.388\ifmmode\pm\else\textpm\fi{}0.004$. The data were analyzed on an electronic digital computer on the basis of the Kotani parameters $Y$, $u$, $x$, and $z$. Information obtained about the nuclear matrix parameters may be summarized as follows: $Y=0.70\ifmmode\pm\else\textpm\fi{}0.20$, $x=0.125\ifmmode\pm\else\textpm\fi{}0.06$, $u=0.125\ifmmode\pm\else\textpm\fi{}0.06$, $z=1.0$. Taken jointly with the $\mathrm{ft}$ value of the 1.49-MeV $\ensuremath{\beta}$ transition these parameters yield the nuclear matrix elements: $\ensuremath{\int}\frac{{B}_{\mathrm{ij}}}{R}=\ifmmode\pm\else\textpm\fi{}(2.9\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, $\ensuremath{\int}\frac{\mathrm{r}}{R}=\ifmmode\pm\else\textpm\fi{}(4.3\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\ensuremath{\int}i\mathrm{o}\ifmmode\times\else\texttimes\fi{}\frac{\mathrm{r}}{R}=\ifmmode\pm\else\textpm\fi{}(3.6\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\ensuremath{\int}i\ensuremath{\alpha}=\ifmmode\pm\else\textpm\fi{}(2.5\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, where $R$ is the nuclear radius of ${\mathrm{Eu}}^{152}$ in units of \ensuremath{\Elzxh}/mc. These results reveal the importance of $\ensuremath{\int}{B}_{\mathrm{ij}}$ relative to the other nuclear matrix elements which contribute to the decay. The experimental value of the matrix element ratio $\frac{\ensuremath{\int}i\ensuremath{\alpha}}{\ensuremath{\int}\mathrm{r}}$ agrees with the prediction of the conserved vector current theory of beta decay.