The island of inversion for neutron-rich nuclei in the vicinity of $N=20$ has become the testing ground par excellence for our understanding and modeling of shell evolution with isospin. In this context, the structure of the transitional nucleus ${}^{29}\mathrm{Mg}$ is critical. The first quantitative measurements of the single-particle structure of ${}^{29}\mathrm{Mg}$ are reported, using data from the $d({}^{28}\mathrm{Mg}, p \gamma ){}^{29}\mathrm{Mg}$ reaction. Two key states carrying significant $\ell =3$ ($f$-wave) strength were identified at $2.40\pm 0.10$ ($J^{\pi }=5/2^{-}$) and $4.28\pm 0.04$ MeV ($7/2^{-}$). New state-of-the-art shell-model calculations have been performed and the predictions are compared in detail with the experimental results. While the two lowest $7/2^{-}$ levels are well described, the sharing of single-particle strength disagrees with experiment for both the $3/2^{-}$ and $5/2^{-}$ levels and there appear to be general problems with configurations involving the $p_{3/2}$ neutron orbital and core-excited components. These conclusions are supported by an analysis of the neutron occupancies in the shell-model calculations.

• Received 3 December 2018

DOI:https://doi.org/10.1103/PhysRevC.99.044320