Nuclear Matrix Elements in the First-Forbidden Beta Decay of theEu152Ground State

The degree of circular polarization $P_c\left({\theta }_{\beta \gamma }\right)$ and the directional correlation $W\left({\theta }_{\beta \gamma }\right)=1+A_2\mathrm{}\left(W\right)\mathrm{}{P}_2\left({cos\theta }_{\beta \gamma }\right)$ were measured in the $3^{-}(1.49\mathrm{}-\mathrm{M}\mathrm{e}\mathrm{V} {\beta }^{-})\to 2^{+}(0.344\mathrm{}-\mathrm{M}\mathrm{e}\mathrm{V} \gamma )\to 0^{+}\beta -\gamma$ cascade leading from the ground state of ${\mathrm{Eu}}^{152}$ to the ${\mathrm{Sm}}^{152}$ ground state. The angle ${\theta }_{\beta \gamma }$ is the angle between the $\beta$ and $\gamma$ momentum vectors. Representative values of $P_c\left({\theta }_{\beta \gamma }\right)$ measured at $\overline{W}=3.20\mathrm{}$ (in units ${\mathit{mc}}^2$) for some average angles ${\overline{\theta }}_{\beta \gamma }$ are: $P_c\left(90\mathrm{}°\right)=-0.01\mathrm{}\pm 0.09$, $P_c\left(130\mathrm{}°\right)=+0.33\mathrm{}\pm 0.07$, $P_c\left(157\mathrm{}°\right)=0.33\mathrm{}\pm 0.07$, $P_c\left(171\mathrm{}°\right)=0.24\mathrm{}\pm 0.10$. Some representative values of the directional correlation coefficient $A_2\mathrm{}\left(W\right)\mathrm{}$ are: $A_2\mathrm{}\left(2.8\right)=-0.335\mathrm{}\pm 0.006$, $A_2\mathrm{}\left(3.15\right)=-0.363\mathrm{}\pm 0.006$, $A_2\mathrm{}\left(3.4\right)=-0.381\mathrm{}\pm 0.005$, $A_2\mathrm{}\left(3.7\right)=-0.388\mathrm{}\pm 0.004$. 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: $Y=0.70\mathrm{}\pm 0.20$, $x=0.125\mathrm{}\pm 0.06$, $u=0.125\mathrm{}\pm 0.06$, $z=1.0\mathrm{}$. Taken jointly with the $\mathrm{ft}$ value of the 1.49-MeV $\beta$ transition these parameters yield the nuclear matrix elements: $\int \frac{B_{\mathrm{ij}}}{R}=\pm (2.9\mathrm{}\pm 0.4)\times {10}^{-3\mathrm{}}$, $\int \frac{\mathrm{r}}{R}=\pm (4.3\mathrm{}\pm 2.3)\times {10}^{-4\mathrm{}}$, $\int i\mathrm{o}\times \frac{\mathrm{r}}{R}=\pm (3.6\mathrm{}\pm 1.9)\times {10}^{-4\mathrm{}}$, $\int i\alpha =\pm (2.5\mathrm{}\pm 1.1)\times {10}^{-4\mathrm{}}$, where $R$ is the nuclear radius of ${\mathrm{Eu}}^{152}$ in units of ħ/mc. These results reveal the importance of $\int B_{\mathrm{ij}}$ relative to the other nuclear matrix elements which contribute to the decay. The experimental value of the matrix element ratio $\frac{\int i\alpha }{\int \mathrm{r}}$ agrees with the prediction of the conserved vector current theory of beta decay.