Ground-state two-proton ($2p$) radioactivity is a rare decay mode found in a few very proton-rich isotopes. The $2p$ decay lifetime and properties of emitted protons carry invaluable information on nuclear structure in the presence of a low-lying proton continuum. The recently measured $2p$ decay of ${}^{67}\mathrm{Kr}$ turned out to be unexpectedly fast. Since ${}^{67}\mathrm{Kr}$ is expected to be a deformed system, we investigate the impact of deformation effects on the $2p$ radioactivity. We apply the recently developed Gamow coupled-channel framework, which allows for a precise description of three-body systems in the presence of rotational and vibrational couplings. This is the first application of a three-body approach to a two-nucleon decay from a deformed nucleus. We show that deformation couplings significantly increase the $2p$ decay width of ${}^{67}\mathrm{Kr}$; this finding explains the puzzling experimental data. The calculated angular proton-proton correlations reflect a competition between $1p$ and $2p$ decay modes in this nucleus.

The structure of the extremely proton-rich nucleus ${{}_8{}^{11}\mathrm{O}}_3$, the mirror of the two-neutron halo nucleus ${{}_3{}^{11}\mathrm{Li}}_8$, has been studied experimentally for the first time. Following two-neutron knockout reactions with a ${}^{13}\mathrm{O}$ beam, the ${}^{11}\mathrm{O}$ decay products were detected after two-proton emission and used to construct an invariant-mass spectrum. A broad peak of width $\sim 3.4\mathrm{MeV}$ was observed. Within the Gamow coupled-channel approach, it was concluded that this peak is a multiplet with contributions from the four lowest ${}^{11}\mathrm{O}$ resonant states: $J^{\pi }=3/2_1^{-}$, $3/2_2^{-}$, $5/2_1^{+}$, and $5/2_2^{+}$. The widths and configurations of these states show strong, nonmonotonic dependencies on the depth of the $p$-${}^9\mathrm{C}$ potential. This unusual behavior is due to the presence of a broad threshold resonant state in ${}^{10}\mathrm{N}$, which is an analog of the virtual state in ${}^{10}\mathrm{Li}$ in the presence of the Coulomb potential. After optimizing the model to the data, only a moderate isospin asymmetry between ground states of ${}^{11}\mathrm{O}$ and ${}^{11}\mathrm{Li}$ was found.

Background: Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space.

Three-body decay is a rare decay mode observed in a handful of unbound rare isotopes. The angular and energy correlations between emitted nucleons are of particular interest, as they provide invaluable information on the interplay between structure and reaction aspects of the nuclear open quantum system. To study the mechanism of two-nucleon emission, we developed a time-dependent approach that allows us to probe emitted nucleons at long times and large distances. We successfully benchmarked the new method against the Green’s function approach and applied it to low-energy two-proton and two-neutron decays. In particular, we studied the interplay between initial-state nucleon-nucleon correlations and final-state interaction. We demonstrated that the time evolution of the two-nucleon wave function is strongly impacted by the diproton/dineutron dynamics and that the correlations between emitted nucleons provide invaluable information on the dinucleon structure in the initial state.