Doppler-Shift Lifetime Measurements in ${\mathrm{Mg}}^{24}$, ${\mathrm{Mg}}^{26}$, and ${\mathrm{Si}}^{28}$

The lifetimes of nuclear levels in ${\mathrm{Mg}}^{24}$, ${\mathrm{Mg}}^{26}$, and ${\mathrm{Si}}^{28}$ have been measured by the Doppler-shift attenuation method. Excited states were produced by inelastic scattering of 22-MeV $\alpha$ particles from the Indiana University cyclotron. $\gamma$-ray spectra were taken in coincidence with $\alpha$-particles striking an annular detector in the backward direction. The Doppler shifts of the $\gamma$-ray peaks were attenuated by thick gold backings behind the targets, allowing the lifetimes of the levels to be calculated in terms of the attenuation and the stopping power of the gold backing. Lifetimes were measured for the 1.37-, 4.12-, and 4.23-MeV levels of ${\mathrm{Mg}}^{24}$; the 1.81- and 2.94-MeV levels of ${\mathrm{Mg}}^{26}$; and the 1.77-, 4.61-, and 4.97-MeV levels of ${\mathrm{Si}}^{28}$. In addition, studies were made of the decay rates of the 5.25-, 6.01-, and 6.43-MeV levels of ${\mathrm{Mg}}^{24}$; the triplet at 4.32-4.35 MeV in ${\mathrm{Mg}}^{26}$; and the 6.889-MeV level in ${\mathrm{Si}}^{28}$. The results for these three even-even $s-d$ shell nuclei are compared with the predictions of several collective theories of nuclear structure, with shell-model calculations based on the $S{U}_3$ classification of states, and with Hartree-Fock calculations.