Probing Configuration Mixing in ${}^{12}\mathrm{Be}$ with Gamow-Teller Transition Strengths

We present a novel technique for studying the quenching of shell gaps in exotic isotopes. The method is based on extracting Gamow-Teller ($\Delta L=0$, $\Delta S=1$) transition strengths [$B(\mathrm{GT})$] to low-lying states from charge-exchange reactions at intermediate beam energies. These Gamow-Teller strengths are very sensitive to configuration mixing between cross-shell orbitals, and this technique thus provides an important complement to other tools currently used to study cross-shell mixing. This work focuses on the $N=8$ shell gap. We populated the ground and 2.24 MeV $0^{+}$ states in ${}^{12}\mathrm{Be}$ using the ${}^{12}\mathrm{B}(1^{+})$ (${}^7\mathrm{Li}$, ${}^7\mathrm{Be}$) reaction at $80\mathrm{MeV}/u$ in inverse kinematics. Using the ground-state $B(\mathrm{GT})$ value from $\beta$-decay measurements ($0.184\pm 0.007$) as a calibration, the $B(\mathrm{GT})$ for the transition to the second $0^{+}$ state was determined to be $0.214\pm 0.051$. Comparing the extracted Gamow-Teller strengths with shell-model calculations, it was determined that the wave functions of the first and second $0^{+}$ states in ${}^{12}\mathrm{Be}$ are composed of $25\pm 5\%$ and $60\pm 5\%$ $(0s{)}^4(0p{)}^8$ configurations, respectively.

Figure 1

(a) Excitation-energy spectrum of ${}^{12}\mathrm{Be}$, excited via the ${}^{12}\mathrm{B}({}^7\mathrm{Li},{}^7\mathrm{Be})$ reaction at $80\mathrm{MeV}/u$ and gated on ${}^{12}\mathrm{Be}$ particles detected in the spectrograph. (b) Laboratory $\gamma$-energy spectrum gated on ${}^{12}\mathrm{Be}$ particles detected in the spectrograph. (c) Same as (a), but also gated on 429 keV $\gamma$ rays in (b). (d) Doppler-reconstructed $\gamma$-ray energy spectrum, gated on region II in (a).

Figure 2

Differential cross sections for the ${}^{12}\mathrm{B}({}^7\mathrm{Li},{}^7\mathrm{Be})$ reaction populating (a) the $0_1^{+}$ and (b) $0_2^{+}$ states of ${}^{12}\mathrm{Be}$. The results of the MDA are also shown in the figures, together with the quality of the fit, expressed in terms of the ${\chi }^2$ per degree of freedom ($n$). The $\Delta J_r=0$ component corresponds to the GT contribution to the excitation.

Figure 3

Ratio of $0_2^{+}$ to $0_1^{+}$ $B(\mathrm{GT})$ values, plotted as a function of the percentage of the (a) $0_1^{+}$ and (b) $0_2^{+}$ state wave function that consist of $0\hslash \omega$ configurations. The red line indicates the $B(\mathrm{GT})$ ratio found in the current work; the shaded area is the error associated with this experimental ratio. The vertical bands correspond to the extracted percentages of $0\hslash \omega$ content (see text).