Mirror symmetry at far edges of stability: The cases of C8 and He8

Missing mass spectroscopy of the unbound ⁸C nucleus was performed by the one-neutron transfer ⁹C(p,d)⁸C reaction at 55 MeV/nucleon. Besides the known ground state, two new resonant states were observed, the first at an excitation energy of 3.40(25) MeV with a width of 3.0(5) MeV, the second at 18.6(5) MeV with a width of 3.9(11) MeV. Spin and parity J^π=2⁺ were assigned to the first resonance from the distorted-wave Born approximation analysis of the experimental differential cross section. The excitation energy of the 2⁺ resonance in ⁸C supports the persistence of the subshell closure at the semimagic number Z = 6, as is the case for N = 6. The mirror energy difference relative to the 2⁺ state in ⁸He, ΔEₓ=-0.14(25) MeV, is compatible with zero. Both states represent resonances in the continuum, unbound by about 1.4 and 6.9 MeV, respectively, above the particle thresholds. A simple theoretical model emphasizes the difference in unboundedness to account for a symmetry in mirror energies. This unique system is expected to provide a salient test of theoretical models, which include the treatment of the continuum.