The ${}^{25}$Mg${(d,}^3$He)${}^{24}$Na reaction has been investigated at 29 MeV incident energy. Spectra were measured at ${\theta }_{\mathrm{lab}}=10\mathrm{}°$ and $18°$. Observations using a split-pole magnetic spectrograph have been made of 56 levels of ${}^{24}$Na in the range of excitation energy between 0 and 7.3 MeV. Most of these have been identified with ${}^{24}$Na levels which have been previously observed by other techniques. From the ratios of the experimental as well as distorted-wave Born approximation (DWBA)-predicted cross sections at the two angles, the population through the pickup of an $l_p=1\mathrm{}$ proton has been established (or confirmed) for the twelve levels at $E_x=3.372\mathrm{}$, 3.745, 3.936, 4.524, 5.192, 5.250, 5.452, 5.846, 5.863, 6.905, 7.084, and 7.246 MeV. Spectroscopic factors were obtained from the comparison of the experimentally measured cross sections at the two angles with the DWBA-predicted cross sections. The experimental values of spectroscopic factors and excitation energies for positive-parity states were compared with the results of a recent, complete $\mathrm{sd}$-shell space, shell-model calculation. In conjunction with the results of various previous works, this comparison leads to the identification of 19 shell-model levels with experimental levels, and thus allows the removal of ambiguities existing in the current literature for the $J^{\pi }$ values of some ${}^{24}$Na states with $E_x<$3.7 MeV.

• Received 14 October 1997

DOI:https://doi.org/10.1103/PhysRevC.57.1256