Electromagnetic transitions between the low-lying levels ofNe21and their relation to parity mixing of the 2.80-MeV12±doublet

The presence of a $J^{\pi }=\frac{1}{2^{+}}-\frac{1}{2^{-}}$ doublet ($\Delta E\simeq 8$ keV) at 2.80 MeV in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ provides an opportunity to further investigate parity mixing of nuclear states. The parity mixing in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ introduces an irregular $M1\mathrm{}$, $E2\mathrm{}$ admixture into the regular, but highly retarded, $E1\mathrm{}$, $M2\mathrm{}$ decay of the $\frac{1}{2^{-}}$ level to the $\frac{3}{2^{+}}$ ground state and can be inferred from the interference between these irregular and regular decays. We consider the dependence of possible ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ parity-mixing observables on the four electromagnetic matrix elements involved in the transition and also methods for determining these matrix elements. The first step towards a measurement of the $\frac{M2\mathrm{}}{E1\mathrm{}}$ mixing ratio is a measurement of the $\frac{E3\mathrm{}}{M2\mathrm{}}$ mixing ratio of the $\frac{1}{2^{-}}\to \frac{5}{2^{+}}$ transition in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ and this is carried out using a $\gamma -\gamma$ correlation utilizing the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(\alpha , n)$ ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ reaction. A large basis SU(3) shell-model calculation is performed to give wave functions for ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ (and ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$) and predictions for the electromagnetic matrix elements relevant to studies of the $\frac{1}{2^{\pm }}$ parity mixing. The parity-mixing matrix element is calculated using a one-body approximation to the parity nonconserving interaction. The calculated matrix elements are compared with the available experimental data on ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$.