Hole states excited by theMg24(p,d)Mg23reaction at 95 MeV

Experimental excitation energies and angular distributions have been obtained for 33 deuteron groups from the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$($p$,$d$) reaction at 94.8-MeV bombarding energy with 80-keV experimental resolution. Energies obtained for states in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$ are in agreement with the sixth compilation of Endt and van der Leun up to 7.25 MeV and the recent unpublished ($p$,$t$) study of Nann et al. up to 9.72 MeV. Energies are determined in the present work for 18 additional groups corresponding to excitations between 9.8 and 13.28 MeV. Angular distributions from 6° to 88° laboratory (momentum transfers up to 660 MeV/c) show characteristic oscillatory signatures for $l=0\mathrm{}$ transitions and broad peaked nonoscillatory behavior for presumed multistep transitions. $l=1\mathrm{} \mathrm{and} 2$ transitions show a very similar exponential falloff with large momentum transfer, but they can be clearly distinguished by their small-angle behavior after division by an empirical exponential factor or by the dominant momentum transfer dependence from a plane-wave analysis. $l=1\mathrm{}$ transitions are observed to deep-hole states at 8.91-, 9.02-, 9.67-, and 10.57-MeV excitation. The angular distributions also lead to very probable assignments of $\frac{5}{2^{-}}$ and $\frac{7}{2^{+}}$ to the 3.97- and 4.68-MeV states of ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$, and are consistent with $\frac{9}{2^{+}}$ and $\frac{11}{2^{+}}$ assignments to the 2.71- and 5.45-MeV states. Distorted-wave Born approximation (DWBA) predictions using optical potentials from published elastic scattering results show rather good agreement with the shapes of the observed angular distributions for $l=2\mathrm{}$ transitions, but spectroscopic factors vary by up to a factor of 3 depending on the deuteron potential employed. $l=0\mathrm{}$ transitions are not fitted in either shape or position of the oscillations, which may be due to the fact that deuteron wave functions derived from elastic scattering are not accurate in the nuclear interior. Reasonable shapes are predicted by preliminary coupled-channel Born approximation (CCBA) analyses for transitions believed to proceed in two steps.