${ \rm \bf Background:}$ 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 $^{ 11}_{ ~8}$O$_3$-$^{ 11}_{ ~3}$Li$_8$ and $^{ 12}_{ ~8}$O$_4$-$^{ 12}_{ ~4}$Be$_8$, which involve the $2p$ emitters $^{ 11}$O and $^{ 12}$O. ${ \rm \bf Purpose:}$ We investigate how continuum effects impact the structure and decay properties of $^{ 11}$O and $^{ 12}$O, and their mirror partners. ${ \rm \bf Methods:}$ 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. ${ \rm \bf Results:}$ 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. ${ \rm \bf Conclusions:}$ 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.
Categories: nucl-th