Single-neutron knockout from intermediate energy beams of ${}^{30,32}\mathrm{Mg}$: Mapping the transition into the “island of inversion”

The breakdown of the $N=20$ magic number in the so-called island of inversion around ${}^{32}\mathrm{Mg}$ is well established. Recently developed large-scale shell-model calculations suggest a transitional region between normal- and intruder-dominated nuclear ground states, thus modifying the boundary of the island of inversion. In particular, a dramatic change in single-particle structure is predicted between the ground states of ${}^{30}\mathrm{Mg}$ and ${}^{32}\mathrm{Mg}$, with the latter consisting nearly purely of 2p-2h $N=20$ cross-shell configurations. Single-neutron knockout experiments on ${}^{30,32}\mathrm{Mg}$ projectiles have been performed. We report on a first direct observation of intruder configurations in the ground states of these very neutron-rich nuclei. Spectroscopic factors to low-lying negative-parity states in the knockout residues are deduced and compare well with shell-model predictions.

Figure 1

Chart of nuclides around the island of inversion. Stable nuclei are shown in black and the island of inversion as discussed in Ref. [10] is shown in gray. The isotopes investigated in the present work are circled. The heavy dotted line represents the recently observed transition from normal-dominated to intruder-dominated ground states in the magnesium and sodium chains. This transition is not yet clearly delineated for the neon isotopes.

Figure 2

Calculated neutron single-particle occupancies. Neutron single-particle occupancies calculated using the USD interaction and the SDPF-M interaction are compared. The independent particle shell model (IPSM) represents normal filling.

Figure 3

Gamma-ray spectrum in coincidence with ${}^{29}\mathrm{Mg}$ fragments. The upper-right panel shows the low-energy region of the spectrum that is Doppler reconstructed using the post-target fragment velocity. The midtarget velocity is used in the Doppler reconstruction of the remainder of the spectrum. Results of a ${\chi }^2$ fit to the low-energy region and to the 0.5- to 4.0-MeV region are overlaid.

Figure 4

Analysis of ${}^{29}\mathrm{Mg}$ 0.336-MeV photopeak. The one-, two-, three-, and four-σ contours are shown illustrating confidence intervals for the simultaneous fit of both intensity and half-life associated with the 0.336-MeV photopeak.

Figure 5

Longitudinal momentum distribution for states populated in the knockout fragment ${}^{29}\mathrm{Mg}$. The corresponding γ-ray energy gate is given at the top of each panel, and calculated distributions assuming $\ell =0$ (solid), $\ell =1$ (dashed), $\ell =2$ (dotted), and $\ell =3$ (dot-dashed) are overlaid. Both $\ell =0$ and $\ell =1$ calculations for the 1.040 distribution include a $50\%\ell =2$ contribution to account for observed indirect feeding.

Figure 6

γ-ray spectrum detected in coincidence with ${}^{31}\mathrm{Mg}$ fragments. The upper panel shows the low-energy region of the spectrum that is Doppler reconstructed using a post-target fragment velocity. The lower panel shows the remainder of the analyzed spectrum, Doppler reconstructed using a midtarget fragment velocity. Results of statistical fits to each region of the spectrum are overlaid with individual photopeak response functions also plotted.

Figure 7

Longitudinal momentum distributions for states populated in the knockout residue ${}^{31}\mathrm{Mg}$. The panel on the left shows the distribution associated with the population of the excited state at 0.221 MeV, whereas the right panel is that for the state at 0.945 MeV. The 0.945-MeV distribution is overlaid with calculated curves assuming $\ell =0$ (solid), $\ell =1$ (dashed), and $\ell =2$ (dotted). The 0.221-MeV distribution is not reproduced by a single $\ell$-value distribution likely due to indirect feeding. This distribution is fit with a combination of $\ell =1$ and $\ell =2$ with a fixed $\ell =3$ component due to known contamination in the γ-ray energy gate.

Figure 8

Observed level scheme for ${}^{31}\mathrm{Mg}$. The $L$ represent multipole orders deduced by lifetime measurements.

Figure 9

Comparison of deduced spectroscopic factors to SDPF-M single-particle occupancies. Deduced spectroscopic factors are indicated by data points with systematic uncertainties shown as gray bars. SDPF-M occupancies are represented by bars. The left panels show a comparison of deduced spectroscopic factors to the lowest $7/2^{-}$ and $3/2^{-}$ states to the respective SDPF-M calculated $0f_{7/2}$ and $1p_{3/2}$ occupancies. The panel on the right shows a comparison of the sum of these deduced spectroscopic strengths to the summed $\mathit{fp}$ SDPF-M single-particle occupancy.