Beta-Gamma Circular-Polarization Correlation and Nuclear Matrix Elements ofAs76

The $\beta -\gamma$ circular-polarization correlation $P_{\gamma }$ for the 2.41-MeV $\beta$ transition of ${\mathrm{As}}^{76}$ has been measured as an average value over the energy interval $E_{\beta }=1.4\mathrm{} \mathrm{to} 2.0$ MeV at an average angle ${\theta }_{\beta \gamma }={158}^{\circ }$. Previous experimental data, this new value for $P_{\gamma }$, and theoretical arguments are used to set limits on the nuclear matrix elements and to investigate the diagonality of the Coulomb Hamiltonian. The analysis shows that matrix elements which change the angular momentum by 0, 1, and 2 units all contribute with approximately equal strength to the transition. The matrix-element analysis indicates that the $A_3$ term in $P_{\gamma }$ is negligible compared to the $A_1$ term. When $A_3$ is set equal to zero, the experimental data give the following value for $P_{\gamma }:P_{\gamma }(1.4\mathrm{} \mathrm{MeV}<E_{\beta }<2.0\mathrm{} \mathrm{MeV}, {\theta }_{\beta \gamma }={180}^{\circ })=0.105\mathrm{}\pm 0.02$.