Study of the Low-Lying Levels of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$ by Angular-Correlation Measurements in the Reaction ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}(d, p\gamma ){}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$

The low-lying excited states of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$ have been studied by means of proton-$\gamma$ angular-correlation measurements in the reaction ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}(d, p\gamma ){}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$, employing the method of Litherland and Ferguson. Protons were detected in a solid-state annular counter near 180° to the beam, and $\gamma$ rays in a NaI(Tl) crystal at seven angles between 0° and 90°. Using an analysis procedure which is independent of any assumption regarding the reaction mechanism, spin assignments of $\frac{3}{2}$, $\frac{5}{2}$, and $\frac{5}{2}$ have been made to the 0.984-, 1.69-, and 1.94-MeV levels. $\gamma$-ray branching ratios of the 1.69- and 1.94-MeV levels have been determined. The multipole mixing ratios of the 1.69→0- and 1.94→0.984-MeV transitions have been deduced, and the latter is in agreement with that obtained from the Nilsson model following the conjecture that 0-, 0.984-, and 1.94-MeV states form the ground-state rotational band.