Exploring the Low-$Z$ Shore of the Island of Inversion at $N=19$

The technique of invariant mass spectroscopy has been used to measure, for the first time, the ground state energy of neutron-unbound ${}^{28}\mathrm{F}$, determined to be a resonance in the ${}^{27}\mathrm{F}+n$ continuum at $2\underline{2}0(\underline{5}0)\mathrm{keV}$. States in ${}^{28}\mathrm{F}$ were populated by the reactions of a $62\mathrm{MeV}/\mathrm{u}$ ${}^{29}\mathrm{Ne}$ beam impinging on a $288\mathrm{mg}/{\mathrm{cm}}^2$ beryllium target. The measured ${}^{28}\mathrm{F}$ ground state energy is in good agreement with USDA/USDB shell model predictions, indicating that $pf$ shell intruder configurations play only a small role in the ground state structure of ${}^{28}\mathrm{F}$ and establishing a low-$Z$ boundary of the island of inversion for $N=19$ isotones.

Figure 1

Corrected TOF for fluorine isotopes produced from ${}^{29}\mathrm{Ne}$.

Figure 2

Simulated resolution and acceptance of the experimental setup. Each colored histogram was generated by simulating a ${}^{28}\mathrm{F}$ breakup at the indicated relative energy and then folding in detector resolution and acceptance cuts. The shaded curve was generated by simulating a ${}^{28}\mathrm{F}$ breakup with the relative energy uniformly distributed from 0–3 MeV and folding in acceptance and resolution. The colored histograms are all normalized to a total area of unity, and the shaded curve was arbitrarily scaled to fit within the same panel.

Figure 3

Measured decay energy spectrum (including smearing from experimental resolution and acceptance) for ${}^{27}\mathrm{F}+n$ coincidences. The filled squares with error bars are the measured data, and the dashed red and dotted blue curves represent the 220 and 810 keV simulation results, respectively. The solid black curve is the sum of the two resonances, with the ratio of 220 keV resonance to the total area being 28%. The filled orange curve is a simulation of a single resonance at 590 keV, and the gray dot-dashed curve is the best fit of a single $s$ wave ($a_s=-0.05\mathrm{fm}$).

Figure 4

Difference between experimental and theoretical (USDA and USDB) binding energies for $N=19$ isotones, $9\le Z\le 17$. The error bars on the data points represent experimental errors only. The blue dotted and red dashed bands represent the respective 170 and 130 keV rms deviations of USDA and USDB interactions. Experimental values, save for $Z=9$, which is from the present work, are taken from Ref. 16 if reported there; otherwise they are from the 2003 Atomic Mass Evaluation [34].