Induced weak currents andβ±−αangular correlations inA=8

$\beta -\alpha$ angular correlations of the form $\omega \left({\theta }_{\beta \alpha }\right)=1+a{cos\theta }_{\beta \alpha }+p{{cos}^2\theta }_{\beta \alpha }$ have been measured as a function of $\beta$ energy for the two decays ${}_{}{}^8{}_{}{}^{}\mathrm{Li}\stackrel{\beta }{\to }{}_{}{}^8{}_{}{}^{}\mathrm{Be}\to 2\alpha$. and ${}_{}{}^8{}_{}{}^{}\mathrm{B}\stackrel{\beta }{\to }{}_{}{}^8{}_{}{}^{}\mathrm{Be}\to 2\alpha$. The results of the angular correlations are considered in a model independent analysis, along with a comparison to model dependent wave function calculations. The $a$ coefficient is a kinematic term that depends on $〈\frac{1}{v^{*}}〉$, where $v^{*}$ is the center of mass velocity of the $\alpha$ particle. A detailed comparison between the experimental results and the theoretical prediction for $a$ shows that the measured kinematic term is (10-15)% smaller than the prediction. The $p$ coefficients arise from induced weak currents. Utilizing the $G$-parity properties of these currents, we discuss the results corresponding to ${\delta }_{\pm }=p_{{}_{}{}^8{}_{}{}^{}\mathrm{Li}}\pm p_{{}_{}{}^8{}_{}{}^{}\mathrm{B}}$. The second order $\beta$ energy dependence in ${\delta }_{-}$ is found to be negligible. Assuming no second order energy dependence, the experimental result is $\frac{\left({\delta }_{-}\right)m_n}{E_{\beta }}=7.0\mathrm{}\pm 0.5=\left(\frac{b}{\mathrm{Ac}}\right)-\left(\frac{d_{\mathrm{II}}}{\mathrm{AC}}\right)$, where $b$ and $d_{\mathrm{II}}$ are the weak magnetism and second class currents, and $c$ is the Gamow-Teller current. The experimental result for $\frac{\left({\delta }_{+}\right)m_n}{E_{\beta }}$ determines the first class induced tensor current