Missing mass spectroscopy on the proton-unbound $^{12}$O nucleus and the breakdown of the $Z$~=~8 shell closure

We will report on the first observation of an excited state in the proton-unbound nucleus $^{12}$O with $Z$~=~8. Recent studies have shown that the shell closure at $N$~=~8 disappears far from stability. A further interest then arises in mirror nuclei, addressing an open question about a persistence or a disappearance of the proton magicity at $Z$~=~8. Level properties of the low-lying states of $^{12}_{~8}$O$_{4}$ should provide an invaluable information since studies on the low-lying intruder states in the mirror partner $^{12}_{~4}$Be$_{8}$ have highlighted the breakdown of the neutron shell closure. However, no definite observation has been made for excited states of $^{12}$O, which lies beyond the proton-drip line. In this study, we applied the missing mass method to the $^{14}$O($p$,$t$)$^{12}$O reaction at 50 MeV/u. The experiment was performed at the GANIL-SPEG facility. The secondary $^{14}$O beam was produced in the SISSI device, and impinged on a 1-mm-thick solid hydrogen target. Recoiling particles were detected by an array of the MUST2 telescopes, each of which was composed of a double-sided silicon strip detector and a CsI calorimeter. A large active area of 100$\times$100 mm$^2$ with a high granularity achieved efficient measurements as well as a good momentum resolution. Based on the experimental result, we will discuss the breakdown of the $Z$~=~8 shell closure in $^{12}$O.