Spectroscopy of ${}^{26}\mathbf{F}$ to Probe Proton-Neutron Forces Close to the Drip Line

A long-lived $J^{\pi }=4_1^{+}$ isomer, $T_{1/2}=2.2(1)\mathrm{ms}$, has been discovered at 643.4(1) keV in the weakly bound ${}_9{}^{26}\mathrm{F}$ nucleus. It was populated at Grand Accélérateur National d’Ions Lourds in the fragmentation of a ${}^{36}\mathrm{S}$ beam. It decays by an internal transition to the $J^{\pi }=1_1^{+}$ ground state [82(14)%], by $\beta$ decay to ${}^{26}\mathrm{Ne}$, or $\beta$-delayed neutron emission to ${}^{25}\mathrm{Ne}$. From the $\beta$-decay studies of the $J^{\pi }=1_1^{+}$ and $J^{\pi }=4_1^{+}$ states, new excited states have been discovered in ${}^{25,26}\mathrm{Ne}$. Gathering the measured binding energies of the $J^{\pi }=1_1^{+}-4_1^{+}$ multiplet in ${}_9{}^{26}\mathrm{F}$, we find that the proton-neutron $\pi 0d_{5/2}\nu 0d_{3/2}$ effective force used in shell-model calculations should be reduced to properly account for the weak binding of ${}_9{}^{26}\mathrm{F}$. Microscopic coupled cluster theory calculations using interactions derived from chiral effective field theory are in very good agreement with the energy of the low-lying $1_1^{+}$, $2_1^{+}$, $4_1^{+}$ states in ${}^{26}\mathrm{F}$. Including three-body forces and coupling to the continuum effects improve the agreement between experiment and theory as compared to the use of two-body forces only.

Figure 1

(a) $\gamma$-ray spectra obtained up to 2 ms after the implantation of ${}^{26}\mathrm{F}$ (upper spectrum), or after the implantation of any nucleus except ${}^{26}\mathrm{F}$ (middle spectrum). The bottom spectrum shows the $\beta$-gated $\gamma$ rays following the implantation of ${}^{26}\mathrm{F}$. (b) Time spectra between implanted ${}^{26}\mathrm{F}$ and $\gamma$ rays, from which half-lives can be deduced. The $4^{+}\to 1^{+}$ transition in ${}^{26}\mathrm{F}$ [643.4(1) keV] and the $4^{+}\to 2_1^{+}$ transition in ${}^{26}\mathrm{Ne}$ [1499.1(4) keV] have the same half-life, while the $2_2^{+}\to 2_1^{+}$ transition in ${}^{26}\mathrm{Ne}$ [1672.5(3) keV] has a larger half-life. (c) $\beta$-gated $\gamma$-ray spectrum following the implantation of ${}^{26}\mathrm{F}$ up to 30 ms. Symbols (colors) indicate which lines correspond to the $\beta$ decay of the $1^{+}$ (black diamonds) and $4^{+}$ (red squares) or to the $\beta$ delayed-neutron branch (blue triangles). The same color codes are used in the decay scheme of Fig. 2. Two lines (green stars) could not be placed in the decay scheme of ${}^{26}\mathrm{F}$.

Figure 2

Decay scheme obtained from the decays of the $4^{+}$ (red) and $1^{+}$ states (black) in ${}^{26}\mathrm{F}$ to ${}^{26}\mathrm{Ne}$ and ${}^{25}\mathrm{Ne}$ (blue). Shell-model predictions obtained with the USDB interaction are shown on the right-hand side. An expanded version of this figure, in which the decay schemes of the $1^{+}$ and $4^{+}$ states are split into two parts, can be seen in the Supplemental Material [27].

Figure 3

Calculated and experimental interaction energies $\mathrm{Int}(1-4)$ in MeV in ${}^{26}\mathrm{F}$. Shell-model calculations are shown in the first column using the USDA or USDB interactions, while the third column shows results obtained with CC calculations. Experimental results are in the center. The thickness of the lines corresponds to $\pm 1\sigma$ error bar.