Structures and decay properties of extremely proton-rich nuclei ${}^{11,12}$O

Abstract

$\mathbf{Background}:$ The recent observation of the unbound nucleus ${}^{11}$O offers the unique possibility to study how the structure and dynamics of two-proton ($2p$) decay is affected by the removal of one neutron from ${}^{12}$O, and provides important information on the Thomas-Ehrman effect in the mirror pairs ${}_8^{11}$O${}_3$-${}_3^{11}$Li${}_8$ and ${}_8^{12}$O${}_4$-${}_4^{12}$Be${}_8$, which involve the $2p$ emitters ${}^{11}$O and ${}^{12}$O. $\mathbf{Purpose}:$ We investigate how continuum effects impact the structure and decay properties of ${}^{11}$O and ${}^{12}$O, and their mirror partners. $\mathbf{Methods}:$ We solve the three-body core-nucleon-nucleon problem using the Gamow coupled-channel (GCC) method. The GCC Hamiltonian employs a realistic finite-range valence nucleon-nucleon interaction and the deformed cores of ${}^{9,10}$C, ${}^9$Li, and ${}^{10}$Be. $\mathbf{Results}:$ We calculate the energy spectra and decay widths of ${}^{11}$O and ${}^{12}$O as well as those of their mirror nuclei. In particular, we investigate the dynamics of the $2p$ decay in the ground state of ${}^{12}$O by analyzing the evolution of the $2p$ configuration of the emitted protons as well as their angular correlations in the coordinate space. We also show how the analytic structure of the resonant states of ${}^{10}$Li and ${}^{10}$N impacts the low-lying states of ${}^{11}$Li and ${}^{11}$O. $\mathbf{Conclusions}:$ We demonstrate that, in both nuclei ${}^{11}$O and ${}^{12}$O, there is a competition between direct and "democratic" $2p$ ground-state emission. The broad structure observed in ${}^{11}$O is consistent with four broad resonances, with the predicted $3/2_1^{-}$ ground state strongly influenced by the broad threshold resonant state in ${}^{10}$N, which is an isobaric analog of the antibound (or virtual) state in ${}^{10}$Li.

9 pages, 8 figures

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