Experimental study of Gamow-Teller transitions via the high-energy-resolution ${}^{18}\mathrm{O}({}^3\mathrm{He},t){}^{18}\mathrm{F}$ reaction: Identification of the low-energy “super” -Gamow-Teller state

Using the high-resolution ${}^{18}\mathrm{O}({}^3\mathrm{He},t){}^{18}\mathrm{F}$ reaction at $0^{\circ }$ and at 140 MeV/nucleon, Gamow-Teller (GT) transitions were studied. A high energy resolution of 31 keV was achieved by applying dispersion matching techniques. The main part of the observed GT transition strength is concentrated in the transition to the ${}^{18}\mathrm{F}$ ground state (g.s.). The absolute values of the reduced GT transition strengths, $B\left(\mathrm{GT}\right)$, were derived up to $E_x=12$ MeV assuming proportionality between the $B\left(\mathrm{GT}\right)$ values and the reaction cross sections at $0^{\circ }$. The $B\left(\mathrm{GT}\right)$ value obtained from the $\beta$ decay of ${}^{18}\mathrm{F}$ (g.s.) $\to {}^{18}\mathrm{O}$ (g.s.) was used to determine the proportionality constant. A total $B\left(\mathrm{GT}\right)$ of 4.06(5) was found and 76(1)% of the strength is concentrated to the ground state of ${}^{18}\mathrm{F}$. The obtained $B\left(\mathrm{GT}\right)$ values were compared with those from the ${}^{18}\mathrm{O}(p,n){}^{18}\mathrm{F}$ reaction and the mirror symmetric ${\beta }^{+}$ decay of ${}^{18}\mathrm{Ne}\to {}^{18}\mathrm{F}$. The candidates for $1^{+}$ states with isospin $T=1$ were identified by comparison with the ${}^{18}\mathrm{O}(p,p^{\prime }$) data. The results of shell-model and quasiparticle-random-phase approximation calculations suggest constructive contributions of various configurations to the ${}^{18}\mathrm{F}$ ground state, suggesting that this state is the low-energy super GT state.

Figure 1

Isospin structure of analogous GT and Fermi transitions among the $A=18$ isobars ${}^{18}\mathrm{O}, {}^{18}\mathrm{F}$, and ${}^{18}\mathrm{Ne}$ with $T_z=+1$, 0, $-1$, respectively. The $J^{\pi }$ values, isospin $T$, and the squared values of the isospin Clebsch-Gordan coefficients are given for the representative states.

Figure 2

Excitation energy spectra of ${}^{18}\mathrm{O}({}^3\mathrm{He},t){}^{18}\mathrm{F}$ measurements for scattering angles $0.0^{\circ }–0.5^{\circ }$ (a) with full vertical scale, (b) with expanded scale ($\times 8$), (c) with more expanded scale ($\times 100$) before the BG subtraction, and (d) with the same scele as (c) but after the BG subtraction. An energy resolution of 31 keV is achieved. For details, see text.

Figure 3

Obtained angular distributions for the low lying states (top) and the corresponding $\mathit{Rr}$ values (bottom). In the left-top panel, the angular distribution of the ${}^{18}\mathrm{F}$ ground state, which is used as the standard for the derivation of $\mathit{Rr}$ ratios, is also shown. For details, see text.

Figure 4

The ${}^{18}\mathrm{O}({}^3\mathrm{He},t){}^{18}\mathrm{F}$ spectra in the energy region of $E_x=6.5–12.5$ MeV for scattering angles (a) $0.0^{\circ }–0.5^{\circ }$, (b) $0.8^{\circ }–1.2^{\circ }$, and (c) $1.6^{\circ }–2.0^{\circ }$. Vertical axes are normalized by the corresponding solid angles. Events from contaminating nuclei are subtracted in all the spectra. The regions where the spectra are distorted by the background subtraction are hatched. The dashed lines show the QFS continuum assumed in the peak decomposition analysis. For details, see text.

Figure 5

The $B\left(\mathrm{GT}\right)$ strength distributions from (a) the present (${}^3\mathrm{He},t$) data, (b) the ($p,n$) data at 135 MeV [19], (c) the ($p,n$) data at 118 MeV [20], (d) the ${}^{18}\mathrm{Ne} \beta$ decay [39, 47], and (e) the $B$($\mathrm{M}{1}_{\sigma }$) values from the ($p,p^{\prime }$) data at 201 MeV [26]. The ground-state strengths are divided by a factor of 5. The horizontal axis of (e) is shifted by 1.1 MeV, so that the analog states are expected to be aligned.

Figure 6

The $B\left(\mathrm{GT}\right)$ strength distributions from (a) the present data and the shell-model calculations using the (b) USDA [49], (c) USDB [49], and (d) modified PSDWBT [50] interactions. The ground-state strengths are divided by a factor of 5.

Figure 7

The Gamow-Teller matrix elements for the three low-lying $1^{+}$ states obtained by the USDA (open circle) and USDB (filled circle) interactions. The corresponding $B\left(\mathrm{GT}\right)$ values are shown together. For details, see text.

Figure 8

Strength distributions of the ${}^{18}\mathrm{O} \to {}^{18}\mathrm{F}$ GT transitions obtained by the HFB $+$ QRPA calculations employing the Skyrme SGII and the surface-type pairing interaction. The IS pairing interaction is included in the QRPA calculations with a factor $f$, a ratio of the strength for the IS pairing interaction to that for the IV pairing interaction. The arrow indicates the IAS obtained at $E_x=5.14$ MeV.