Lifetimes of the Lowest52+and92+States of the Mirror PairNa23-Mg23

The lifetimes of the ${\frac{5}{2}}^{+}$ and ${\frac{9}{2}}^{+}$ members of the $K^{\pi }={\frac{3}{2}}^{+}$ ground-state rotational band in the mirror pair ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$-${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$ have been measured via the Doppler-shift attenuation method. The reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}+{}_{}{}^{12}{}_{}{}^{}\mathrm{C}={}_{}{}^{23}{}_{}{}^{}\mathrm{Na}+ p$ or ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}+ n$ were used and line shapes of the decay $\gamma$ rays were observed in singles for recoil into Al and Ni backings. The results are 1.63±0.20 and 2.00±0.24 psec for the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$ ${\frac{5}{2}}^{+}$ first excited states and 0.11±0.02 and 0.08±0.02 psec for the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$ ${\frac{9}{2}}^{+}$ states. These results are compared to the predictions of the Nilsson model. The separation of the isoscalar and isotensor components of the $M$ 1 rates is discussed as well as the separation of the spin and orbital contributions to the isotensor component. Incidental to this work, the energies of the first excited states were determined as 439.80 ± 0.15 keV (${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$) and 450.70±0.15 keV (${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$), and the ${\frac{9}{2}}^{+}\to {\frac{7}{2}}^{+}$ transition energies were measured with comparable accuracy.