High-resolution study of ${}^{11}\mathrm{B}$ to ${}^{11}\mathrm{C}$ Gamow-Teller strengths as a test case of ab initio shell-model calculations

A high energy-resolution ${}^{11}\mathrm{B}\left({}^3\mathrm{He},t\right){}^{11}\mathrm{C}$ experiment was performed at $0°$ and an intermediate incident energy of $140\mathrm{MeV}∕\mathrm{nucleon}$ for the study of precise Gamow-Teller (GT) transition strengths. Two doublet states at $\approx 4.5$ and $\approx 8.4\mathrm{MeV}$ were clearly resolved with a resolution of $45\mathrm{keV}$. The strengths are compared with a calculation using an ab initio no-core shell model, which became available for the $A=11$ system recently. It was found that a calculation including a three-nucleon interaction better reproduces the observed GT transition strengths.

Figure 1

(Color online) Spectra of the ${}^{11}\mathrm{B}\left({}^3\mathrm{He},t\right){}^{11}\mathrm{C}$ reaction of (a) the range up to the excitation energy of $16\mathrm{MeV}$ for scattering angles $\Theta ⩽0.5°$, and (b) expanded $6–10\mathrm{MeV}$ region. Excitation energies (in MeV) and $J^{\pi }$ values are indicated.

Figure 2

(Color online) Experimental and shell-model $B\left(\mathrm{GT}\right)$ distributions. The $J^{\pi }$ values of states are indicated. The $B\left(\mathrm{GT}\right)$ distributions are shown (a) for the present ${}^{11}\mathrm{B}\left({}^3\mathrm{He},t\right){}^{11}\mathrm{C}$ experiment, (b) for a NCSM calculation by Navrátil and Ormand including the TNI [1], (c) for a NCSM calculation without a TNI [1], and (d) for a shell-model calculation obtained by using the Cohen-Kurath interaction (from Ref. 7). Note the change in size of the panels.