Two-Neutron Halo is Unveiled in ${}^{29}\mathrm{F}$

We report the measurement of reaction cross sections (${\sigma }_R^{\mathrm{ex}}$) of ${}^{27,29}\mathrm{F}$ with a carbon target at RIKEN. The unexpectedly large ${\sigma }_R^{\mathrm{ex}}$ and derived matter radius identify ${}^{29}\mathrm{F}$ as the heaviest two-neutron Borromean halo to date. The halo is attributed to neutrons occupying the $2p_{3/2}$ orbital, thereby vanishing the shell closure associated with the neutron number $N=20$. The results are explained by state-of-the-art shell model calculations. Coupled-cluster computations based on effective field theories of the strong nuclear force describe the matter radius of ${}^{27}\mathrm{F}$ but are challenged for ${}^{29}\mathrm{F}$.

Figure 1

(a) Schematic view of the experimental setup. The nuclei ${}^{27,29}\mathrm{F}$ are transported from the focal plane F0 to F8, where the reaction target is located. Unreacted ${}^{29}\mathrm{F}$ is identified using the ZDS from F8 to F11. Particle identification (b) before the carbon reaction target at F8 and (c) after the target at F11 with ${}^{29}\mathrm{F}$ events selected before the target.

Figure 2

Measured reaction cross sections of fluorine isotopes with a carbon target at $E/A\approx 240\mathrm{MeV}$. The red filled circles are data of the present work. The open blue squares are from Ref. [33]. The data show statistical and systematic uncertainties. The dashed line shows the trend of $A^{2/3}$ relative evolution normalized for best fit to ${}^{19–27}\mathrm{F}$.

Figure 3

The red lines show Glauber calculation of ${\sigma }_R$ of ${}^{29}\mathrm{F}+\mathrm{C}$ with ${}^{27}\mathrm{F}+n+n$ densities at $E/A=246\mathrm{MeV}$ (midtarget energy) for different fractions ($\alpha$), (see text for definition) of neutrons in the $2p_{3/2}$ orbital. The solid (dashed) lines are for $S_{2n}$/2= 0.7(3) MeV. The horizontal shaded band corresponds to the measured ${\sigma }_R^{\mathrm{ex}}$.

Figure 4

Comparison between the experimental values for ${\sigma }_R^{\mathrm{ex}}$ and $R_m^{\mathrm{ex}}$ and various theoretical results. The data include statistical and systematic uncertainties. (a) Comparison of measured ${\sigma }_R^{\mathrm{ex}}$ (black filled squares) with Glauber calculations using density distributions from the shell model based on the SDPF-MU (open blue circles) and the EEdf1 (magenta square) interaction. (b) Comparison of derived $R_m^{\mathrm{ex}}$ for ${}^{27,29}\mathrm{F}$ (black filled squares) with predictions from shell-model calculations using the SDPF-MU interaction (open blue circles) and the EEdf1 interaction (magenta squares). Coupled-cluster results based on the chiral ${\mathrm{NNLO}}_{\mathrm{sat}}$ ($\mathrm{\Delta }\text{−}{\mathrm{NNLO}}_{\mathrm{GO}}$) interaction are shown as a green band (open black-white band). The cyan band is the result from a particle-rotor model.