Low-lying states in ${}^{12}\mathrm{Be}$ using one-neutron transfer reaction

A new one-neutron adding reaction on ${}^{11}\mathrm{Be}$ was performed at $26.9A$ MeV. The elastic-scattering data was measured simultaneously to determine the target component and optical potentials for the entrance channel. A special isomer-tagging method was used to determine the cross sections for the $0_2^{+}$ state. Based on the ratio of the $s$-wave spectroscopic factors of the $0_1^{+}$ and $0_2^{+}$ states, along with the previously reported $p$-wave intensities, the $s$- and $d$-wave components of these two states were obtained and compared with shell-model calculations using various interactions. The result shows a dominant $d$-wave strength in the ground state of ${}^{12}\mathrm{Be}$, and reveals the dominance of $sd$- and $sp$-single-particle configurations in the $2^{+}$ and $1^{-}$ state of ${}^{12}\mathrm{Be}$, respectively. Together with the configuration mixing analysis, the relative spectroscopic factors, which are shown to be less sensitive to the different choice of optical potentials, provide important insights on the wave functions for the low-lying states of ${}^{12}\mathrm{Be}$.

Figure 1

Schematic sketch of the experimental setup for the present measurement.

Figure 2

The elastic-scattering differential cross sections of (a) ${}^{11}\mathrm{Be}+p$ and (b) ${}^{11}\mathrm{Be}+d$ at $26.9A$ MeV. The data points have been divided by the Rutherford scattering cross sections. The black dash-dotted line in (a) donates the calculation result using the CH89 potential, while the red solid line is the result after application of the renormalization parameters (see details in the text). The red dashed line in (b) represents the calculation using the optical model with the DA1p potential.

Figure 3

(a) The PID in coincidence with the protons detected by the ADSSD. (b) Summed energy spectrum of the protons in ADSSD and the corresponding Be isotopes in TELE0. From high to low energies, three peaks mostly correspond to the ${}^{12}\mathrm{Be}$, ${}^{11}\mathrm{Be}$, and ${}^{10}\mathrm{Be}$ events in (a).

Figure 4

(a) The measured proton energies versus the laboratory angles, gated on the ${}^{12}\mathrm{Be}$ in the TELE0. The red solid lines illustrate the calculated kinematics of the ${}^{11}\mathrm{Be}(d,p)$ transfer reaction to the $0_1^{+}$ (g.s.) and the 2.251-MeV excited state. (b) The excitation energy spectrum of ${}^{12}\mathrm{Be}$ deduced using the protons in (a). The dotted curve in the inset shows the events in coincidence with the 0.511-MeV $\gamma$ rays detected by the scintillation counters. (c) The $\gamma$-ray energy spectrum in coincidence with ${}^{12}\mathrm{Be}+p$ events within the $3\mu \mathrm{s}$ time window.

Figure 5

Measured differential cross sections of the ${}^{11}\mathrm{Be}(d,p){}^{12}\mathrm{Be}$ reaction at $26.9A$ MeV (solid dots), together with the FR-ADWA calculations normalized using the SFs, for (a) the ground state ($0_1^{+}$), (b) the isomeric state ($0_2^{+}$), and (c) the summed $2^{+}$ and $1^{-}$ states. $\ell$ in each figure stands for the transferred orbital angular momentum.

Figure 6

The presently measured ${}^{11}\mathrm{Be}(d,p){}^{12}\mathrm{Be}$ differential cross sections for the (a) first and (b) second $0^{+}$ states together with calculations using different OPs. The calculations using the local or global potentials are fitted to the data to extract the respective SFs. See text for more details.

Figure 7

(a) The level schemes of the low-lying states in ${}^{12}\mathrm{Be}$ from the experimental data and shell-model calculations with WBP [22] or YSOX Hamiltonian. The individual $s$-, $p$-, and $d$-wave intensities for the $0_1^{+}$ and $0_2^{+}$ states deduced from experiments (b) compared to those calculated using YSOX interaction in Case1 (c) and Case2 (d).