New investigation of low-lying states in ${}^{12}\mathrm{Be}$ via a ${}^2\mathrm{H}({}^{13}\mathrm{B},{}^3\mathrm{He})$ reaction

We investigate the low-lying positive-parity states in ${}^{12}\mathrm{Be}$, which are populated by the ${}^2\mathrm{H}({}^{13}\mathrm{B}$, ${}^3\mathrm{He})$ reaction via $l=1$ proton transfer for the first time using a radioactive beam ${}^{13}\mathrm{B}$ at 23 MeV/nucleon. Spectroscopic factors and excitation energies of these states are in reasonable agreement with the shell model predictions. Besides two bound states, we observe a resonant state at $E_x=4.8\pm 0.1\mathrm{MeV}$ with an intrinsic width of $0.42\pm 0.28$ MeV, which predominately decays via one neutron to the bound states in ${}^{11}\mathrm{Be}$. It most likely corresponds to the $E_n=1.24\mathrm{MeV}$ state observed in the previous one-proton removal reaction. The spin-parity of $2^{+}$ is tentatively assigned to this resonance according to the analysis of its angular distributions as well as the theoretical calculations, including shell model and Gamow coupled-channel approach.

Figure 1

Energy level scheme of (a) ${}^{12}\mathrm{Be}$, (b) ${}^{11}\mathrm{Be}$, and (c) the possible decay path of the $E_n=1.24\mathrm{MeV}$ state in ${}^{12}\mathrm{Be}$, which was observed from the $1p$ removal reaction [20]. The excitation energy of the $E_n=1.24\mathrm{MeV}$ state was not determined. See text for the details.

Figure 2

Schematic view of the experimental setup.

Figure 3

Deuterons elastically scattered from ${}^{13}\mathrm{B}$ in the particle identification (PID) spectrum measured by T2. The inset shows the PID spectrum measured by T0, where the boron isotopes are shown in coincidence with deuterons.

Figure 4

Bidimensional plot of energy vs angle in the laboratory frame for the recoil deuterons in coincidence with the boron isotopes at forward angles. The kinematic loci for the elastic scattering of ${}^{13}\mathrm{B}+d$ are shown as the red solid curve.

Figure 5

Excitation energy spectrum of ${}^{13}\mathrm{B}$ reconstructed from energies and angles of the scattered deuterons measured by T2. The inset shows more details of the energy spectrum for inelastic scattering.

Figure 6

Elastic scattering differential cross sections, relative to the Rutherford cross sections. Two sets of global optical potentials were employed for the theoretical calculations. See text for more details.

Figure 7

PID spectrum of the beryllium isotopes detected by T0 in coincidence with the light charged particles measured in T1. The inset shows the measured helium isotopes by T1.

Figure 8

In coincidence with the beryllium isotopes, the energies of ${}^3\mathrm{He}$ as a function of angles in the laboratory frame. The red lines illustrate the calculated kinematics of the ${}^2\mathrm{H}({}^{13}\mathrm{B},{}^3\mathrm{He}){}^{12}\mathrm{Be}$ transfer reaction to the states of interest in ${}^{12}\mathrm{Be}$.

Figure 9

Excitation energy spectrum of ${}^{12}\mathrm{Be}$ reconstructed from the energies and angles of ${}^3\mathrm{He}$ at $24\text{−}{44}^{\circ }$. The blue dashed curves show the fitted peaks for each state, and the red solid curve shows the sum of blue dashed curves. The number of degrees of freedom (ndf) corresponds to the number of data points used in the fit minus the number of free parameters.

Figure 10

Differential cross sections of the ${}^2\mathrm{H}({}^{13}\mathrm{B},{}^3\mathrm{He}){}^{12}\mathrm{Be}$ transfer reaction to (a) the $0_1^{+}$, (b) the mixed state of $0_2^{+}$ and $2_1^{+}$, and (c) the 4.8-MeV state in ${}^{12}\mathrm{Be}$. The $0_2^{+}$ state can not be separated from the $2_1^{+}$ state, so they were fitted as one peak in Fig. 9. The excitation energies as well as the spin parities of each state in ${}^{12}\mathrm{Be}$, and the transferred orbital angular momentum $l$, which were used in the calculations with the codes of FRESCO and TWOFNR, are given in the figures. Note that the calculation results using the finite-range transfer interactions have been averaged over an angular range corresponding to the angular acceptance for each data point.