Evolution of single-particle structure near the $N=20$ island of inversion

The single-particle properties of ${}^{29}\mathrm{Mg}$ have been investigated via a measurement of the ${}^{28}\mathrm{Mg}(d,p){}^{29}\mathrm{Mg}$ reaction, in inverse kinematics, using the ISOLDE Solenoidal Spectrometer. The negative-parity intruder states from the $fp$ shell have been identified and used to benchmark modern shell-model calculations. The systematic data on the single-particle centroids along the $N=17$ isotones show good agreement with shell-model predictions in describing the observed trends from stability toward ${}^{25}\mathrm{O}$. However, there is also evidence that the effect of the finite geometry of the nuclear potential is playing a role on the behavior of the $p$ orbitals near the particle-emission threshold.

Figure 1

Excitation spectrum for states populated in the ${}^{28}\mathrm{Mg}(d,p){}^{29}\mathrm{Mg}$ reaction at 9.47 MeV/$u$ across all the array. States are labeled with energy in keV and angular-momentum transfer. The dotted line indicates the neutron-separation energy. Gaussian fits to peaks are overlaid for bound (red) and unbound (purple) states.

Figure 2

Angular distributions for states observed in the ${}^{28}\mathrm{Mg}(d,p){}^{29}\mathrm{Mg}$ reaction, labeled by energy in keV. The lines are DWBA calculations for angular-momentum transfer with $\ell =0$ (black), 1 (green dashed), 2 (red hatched), and 3 (blue). The solid red line for the ground-state doublet denotes a sum of the two distributions. Where new assignments are made, possible DWBA fits are shown with the value of the reduced ${\chi }^2$.

Figure 3

Spectroscopic factors from the present work (EXP) for states with $J^{\pi }=1/2^{+}$ (unfilled black), $1/2,3/2^{-}$ (unfilled/filled green), $3/2,5/2^{+}$ (filled/unfilled red), and $5/2,7/2^{-}$ (unfilled/filled blue), with statistical errors. Spectroscopic factors from shell-model calculations are given for the interactions described in the text. The states at 3906 and 4045 keV have been shown here as $1/2^{-}$ and $3/2^{-}$ respectively, but the reverse order is equally possible.

Figure 4

(Top) Binding energy of single-particle centroids for $J^{\pi }=3/2^{+}$ ($\square$), $7/2^{-}$ ($◯$), $3/2^{-}$ ($▵$), and $1/2^{-}$ ($▿$) in $N=17$ isotones. Centroids for $J^{\pi }=1/2^{-}\mathrm{and}3/2^{-}$, including states above 5.5 MeV, are denoted by $⊳$. Data for ${}^{31}\mathrm{Si}$ and ${}^{33}\mathrm{S}$ are from Refs. [32, 33, 34]. Bands represent calculations using the FSU interaction, with widths representing experimental uncertainties in ${}^{31}\mathrm{Si}$, onto which they are shifted. (Bottom) Calculated nucleon occupancies for $N=17$ isotones from FSU interaction (lines). Symbols represent neutron occupancies extracted from the data.

Figure 5

Binding energies calculated using Woods-Saxon formalism with fixed geometry (see text); bands include experimental uncertainties for ${}^{31}\mathrm{Si}$, to which the calculations have been fixed. Symbols have the same meaning as Fig. 4.