Low-$Z$ shore of the “island of inversion” and the reduced neutron magicity toward ${}^{28}\mathrm{O}$

The two odd-even fluorine isotopes ${}^{27,29}\mathrm{F}$ were studied via in-beam $\gamma$-ray spectroscopy at the RIKEN Radioactive Isotope Beam Factory. A secondary beam of ${}^{30}\mathrm{Ne}$ was used to induce one-proton and one-proton–two-neutron removal reactions on carbon and polyethylene targets at midtarget energies of 228 MeV/$u$. Excited states were observed at 915(12) keV for ${}^{27}\mathrm{F}$ and at 1080(18) keV for ${}^{29}\mathrm{F}$. Both were assigned a $1/2_1^{+}$ spin and parity. The low transition energy for ${}^{29}\mathrm{F}$ largely disagrees with shell model predictions restricted to the $sd$ model space. Calculations using effective interactions that include the neutron $pf$ shell indicate that the $N=20$ gap is quenched for ${}^{29}\mathrm{F}$, thus extending the “island of inversion” to isotopes with proton number $Z=9$. Variations of the $N=20$ gap further reveal a strong correlation to the $1/2_1^{+}$ level energy in ${}^{29}\mathrm{F}$ and suggest a persistent reduced neutron gap for ${}^{28}\mathrm{O}$.

Figure 1

Particle identification plot behind the secondary target with ${}^{30}\mathrm{Ne}$ selected in BigRIPS and ZeroDegree tuned for ${}^{29}\mathrm{F}$. Secondary beams identified in BigRIPS are shown in the inset.

Figure 2

Doppler-corrected $\gamma$-ray spectra with the condition $M_{\gamma }<4$ in coincidence with ${}^{27}\mathrm{F}$ [upper panel (a)] and ${}^{29}\mathrm{F}$ [lower panel (b)] reaction residues from the ${}^{30}\mathrm{Ne}$ secondary beam. The black solid lines show the sum of fitted experimental exponential background (blue dotted) and simulated, Doppler-shift corrected DALI2 response functions (red dotted) for transition energies of 915 and 1080 keV, respectively. Conditions on $M_{\gamma }$ were removed for the insets (c) and (d).

Figure 3

Experimental energy levels of ${}^{27,29}\mathrm{F}$ compared with shell model calculations using the USDA/USDB and SDPF-M effective interactions. Only SDPF-M provides an adequate description of the first excited state in ${}^{29}\mathrm{F}$. Dashed lines are drawn to guide the eye.

Figure 4

Correlation between first excited states [top panel (a)] and $0p0h$ wave-function compositions of ground and first excited state [bottom panel (b)] for ${}^{29}\mathrm{F}$ and ${}^{28}\mathrm{O}$ as function of a varied $N=20$ gap with the SDPF-M interaction. Calculated two-neutron separation energies for ${}^{29}\mathrm{F}$ are also shown. Original SDPF-M values correspond to ${\mathrm{\Delta }}_{\mathrm{gap}}=0$.