Beta-Gamma Directional Correlation inLa140

The directional correlation between the nonunique first-forbidden outer beta group of end-point energy 2.175 MeV in ${\mathrm{La}}^{140}$ and the 1.6-MeV cascade gamma ray in ${\mathrm{Ce}}^{140}$ has been measured at nine beta energies. The measured beta-gamma correlation coefficient $\epsilon$ ranges from (0.080±0.010) to (0.111±0.020) in the beta-energy interval 1.6 to 2 MeV. Taking account of the existing data on shape correction factor and also the beta-gamma circular polarization coefficient $\omega$ for $\theta =160\mathrm{}°$ and $W=4.2\mathrm{}$, the relevant first-forbidden beta-decay matrix-element ratios have been extracted; the ratios of the matrix elements are (in Kotani's notation) $x=-0.33\mathrm{}\pm 0.15$, $u=-0.06\mathrm{}\pm 0.06$, and $Y=-1.50\mathrm{}\pm 0.20$. Absolute values of the matrix elements were obtained from the observed $\mathrm{ft}$ value as $\frac{\left|\int B_{\mathrm{ij}}\right|}{R}=(3.3\mathrm{}\pm 0.5)\times {10}^{-2\mathrm{}}$, $\frac{\left|\int \mathrm{r}\right|}{R}=(1.3\mathrm{}\pm 0.6)\times {10}^{-2\mathrm{}}$, $\frac{\left|\int i\sigma \times \mathrm{r}\right|}{R}=(0.2\mathrm{}\pm 0.2)\times {10}^{-2\mathrm{}}$, $\left|\int i\alpha \right|=(4.3\mathrm{}\pm 1.5)\times {10}^{-3\mathrm{}}$. A cancellation among the vector-type matrix elements is apparently the cause of the deviation from the $\xi$ approximation in this case.