The unbound ${}^{12}\mathrm{O}$ nucleus was studied via the two-neutron transfer $(p,t)$ reaction in inverse kinematics using a radioactive ${}^{14}\mathrm{O}$ beam at 51 MeV/u. Excitation energy spectra and differential cross sections were deduced by the missing mass method using MUST2 telescopes. We achieved much higher statistics compared to the previous experiments of ${}^{12}\mathrm{O}$, which allowed accurate determination of resonance energy and unambiguous spin and parity assignment. The ${}^{12}\mathrm{O}$ resonance previously reported using the same reaction was confirmed at an excitation energy of $1.62\pm 0.03\left(\mathrm{stat}.\right)\pm 0.10\left(\mathrm{syst}.\right)$. MeV and assigned spin and parity of $0^{+}$ from a distorted-wave Born approximation analysis of the differential cross sections. Mirror symmetry of ${}^{12}\mathrm{O}$ with respect to its neutron-rich partner ${}^{12}\mathrm{Be}$ is discussed from the energy difference of the second $0^{+}$ states. In addition, from systematics of known $0^{+}$ states, a distinct correlation is revealed between the mirror energy difference and the binding energy after carrying out a scaling with the mass and the charge. We show that the mirror energy difference of the observed $0^{+}$ state of ${}^{12}\mathrm{O}$ is highly deviated from the systematic trend of deeply bound nuclei and in line with the scaling relation found for weakly bound nuclei with a substantial $2s_{1/2}$ component. The importance of the scaling of mirror asymmetry is discussed in the context of ab initio calculations near the drip lines and universality of few-body quantum systems.

• Received 30 November 2015

DOI:https://doi.org/10.1103/PhysRevC.93.024316