Pairing-Model Calculation of Nuclear Matrix Elements in the Decay ofAs74

Abstract

The matrix elements $C_A\int \mathbf{\sigma }\mathbf{·}\mathbf{r}$, $C_A\int \mathbf{r}$, $C_V\int \mathbf{i}\mathbf{\sigma }\times \mathbf{r}$, and $C_A\int B_{\mathrm{ij}}$ are calculated for ${}_{}{}^{74}{}_{}{}^{}\mathrm{As}$, using the pairing model. $C_V\int \mathbf{i}\mathbf{\alpha }$ is determined from the conserved vector current theory, and $C_A\int \mathbf{i}{\gamma }_5$ from $\beta -\gamma$ angular correlation data. The ratio of the $\frac{{\left(\int B_{\mathrm{ij}}\right)}^1}{{\left(\int B_{\mathrm{ij}}\right)}^2}$ for the $\beta$ transitions to the ground state and first excited state, respectively, of ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ is calculated from these matrix elements and the $\beta$ intensities. This ratio is also calculated solely from the model and compared with the above ratio to check the internal consistency of the method. The results show that better agreement is obtained if the effect of phonon-quasiparticle coupling is included.