Missing mass spectroscopy of the unbound ${}^8\mathrm{C}$ nucleus was performed by the one-neutron transfer ${}^9\mathrm{C}(p,d){}^8\mathrm{C}$ 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 $J^{\pi }=2^{+}$ 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 ${}^8\mathrm{C}$ 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 ${}^8\mathrm{He}, \mathrm{\Delta }{E}_{\mathrm{x}}=-0.14$(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.

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• Energy levels
• Nuclear structure & decays
• Proton emission
• 6 ≤ A ≤ 19
• Nuclear data analysis & compilation
• Radioactive beams