Structure of ${}^{28}\mathrm{Mg}$ and influence of the neutron $pf$ shell

Gamma-ray spectroscopy and lifetime measurements using the Doppler shift attenuation method (DSAM) were performed on the nucleus ${}^{28}\mathrm{Mg}$ near the $N=20$ “island of inversion,” which was populated using a ${}^{12}\mathrm{C}({}^{18}\mathrm{O},2\mathrm{p}){}^{28}\mathrm{Mg}$ fusion-evaporation reaction to investigate the impact of shell evolution on its high-lying structure. Three new levels were identified at 7203(3), 7747(2), and 7929.3(12) keV along with several new gamma rays. A newly extracted $B(E2;4_1^{+}\to 2_1^{+})$ of 42(7) $e^2{\mathrm{fm}}^4$ indicates reduced collectivity in the yrast band at high spin, consistent with ab initio symmetry adapted no-core shell model (SA-NCSM) calculations. At high excitation energy, evidence for the population of intruder orbitals was obtained through identification of negative parity levels $[I^{\pi }={(0,4)}^{-}$, ${(4,5)}^{-}]$. Calculations using the SDPF-MU interaction indicate that these levels arise from single neutron excitation to the $pf$ shell and provides evidence for the lowering of these intruder orbitals approaching the island of inversion.

Figure 1

Scheme of observed levels and gamma rays in ${}^{28}\mathrm{Mg}$. Arrow widths specify relative intensities of gamma rays. Spin-parity values are taken from Table 3 and Ref. [19].

Figure 2

Background subtracted gamma-ray coincidence spectra showing observed levels in ${}^{28}\mathrm{Mg}$, after gating on the $4_1^{+}\to 2_1^{+}$ transition (top) and the $2_1^{+}\to 0_1^{+}$ transition (bottom), from Doppler corrected thin target data. Inset figures show the high energy region of the corresponding spectrum.

Figure 3

Comparison of line shapes from data and geant4 simulations for the gamma rays depopulating the 4021.4(3) and 6528.2(9) keV levels in ${}^{28}\mathrm{Mg}$, shown for each detector group. ${\tau }_{\text{mean}}$ values of 180 fs for the 4021.4(3) keV level and 190 fs for the 6528.2(9) keV level were used. The total simulated line shape contains contributions from the decay of both levels, as well as feeding of the 4021.4(3) keV level from the 5184.3(5) and 6528.2(9) keV levels.

Figure 4

Angular distributions of the 2547.6(3), 3726(2), and 3907.6(12) keV gamma rays observed in this work, normalized to the relative efficiency of each ring of TIGRESS cores. Fits to Eq. (1) are shown.

Figure 5

Left: systematics of known yrast states in $Z=12$ isotopes [18, 19, 31, 32]. Right: systematics of known yrast states in $N=16$ isotones [19, 20, 33]. Levels from this work which are candidates for the $6_1^{+}$ $[I^{\pi }=\left(6^{+}\right)$, 7929.3(12) keV] and $5_1^{-}$ $[I^{\pi }={(4,5)}^{-}$, 6528.2(9) keV] levels in ${}^{28}\mathrm{Mg}$ are shown.

Figure 6

Top: ${\chi }^2$ surface plot in gamma ray energy and mean lifetime for the 7929.3(12) keV level in ${}^{28}\mathrm{Mg}$, showing a surface fit to the simulated data points. Bottom: Projection of the ${\chi }^2$ surface at the fit minimum $E_{\gamma }=3.911\left(4\right)\mathrm{MeV}$.

Figure 7

Background subtracted gamma-ray coincidence spectrum following gating on the 1356.3(12) gamma ray in ${}^{28}\mathrm{Mg}$.

Figure 8

Line shape of the 4664.9(12) keV gamma ray observed in background subtracted thin target and summed DSAM target data.

Figure 9

Experimentally determined $B\left(E2\right)$ values for the yrast band of ${}^{28}\mathrm{Mg}$, from this work and previous studies [13, 14], compared to calculated values derived from various interaction models.

Figure 10

Comparison of experimentally determined level energies in ${}^{28}\mathrm{Mg}$ to calculated values derived from ab initio SA-NCSM calculations, with $\hslash \omega =15\mathrm{MeV}$ in 9 major harmonic oscillator shells. Bands are labeled based on the major shape contributions to the lowest $0^{+}$ state, which remain roughly the same for the higher spin states (see also Table 6). Energies of excited $0^{+}$ levels in ${}^{28}\mathrm{Mg}$ are taken from Ref. [19], all other levels were observed in this work.

Figure 11

Comparison of experimentally determined yrast level energies in ${}^{28}\mathrm{Mg}$ to calculated values derived from shell models in $sd$ and $sdpf$ valence spaces. Connections are drawn between calculated levels and their closest candidates in the experimental data. Negative parity levels are denoted in light grey. The known $I^{\pi }=1^{+}$ level in ${}^{28}\mathrm{Mg}$ is taken from Ref. [19]; all other levels were observed in this work. The observed $I^{\pi }=3^{-},\left(4^{+}\right)$ levels near 5.2 MeV are slightly offset in energy for readability.

Figure 12

Calculated neutron occupancies in the $pf$ shell using the SDPF-MU interaction.

Figure 13

Proton and neutron effective single-particle energies for ${}^{28}\mathrm{Mg}$ from the SDPF-MU interaction, with intruder orbitals denoted in light grey.