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.Purpose: To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the new framework against the complex-energy Gamow Shell Model (GSM). Methods:The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering and Gamow states. Results:We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results. Conclusions:We have demonstrated that a three-body GSM formalism explicitly constructed in cluster-orbital shell model coordinates provides similar results to a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for A = 6 systems and 26 O show that nucleonnucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, efficient, and can be extended by introducing a microscopic model of the core.

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 O3-11 3 Li8 and 12 8 O4-12 4 Be8, which involve the 2p emitters 11 O and 12 O.Purpose: We investigate how continuum effects impact the structure and decay properties of 11 O and 12 O, and their mirror partners. 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. 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. 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.

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}Kr turned out to be unexpectedly fast. Since ^{67}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}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 11 8 O3, the mirror of the two-neutron halo nucleus 11 3 Li8, has been studied experimentally for the first time. Following two-neutron knockout reactions with a 13 O beam, the 11 O decay products were detected after two-proton emission and used to construct an invariant-mass spectrum. A broad peak of width ∼3 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 O resonant states: J π =3/2 − 1 , 3/2 − 2 , 5/2 + 1 , and 5/2 + 2. The widths and configurations of these states show strong, non-monotonic dependencies on the depth of the p-9 C potential. This unusual behavior is due to the presence of a broad threshold resonant state in 10 N, which is an analog of the virtual state in 10 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 O and 11 Li was found.

Particle-decaying states of the light nuclei 11,12 N and 12 O were studied using the invariant-mass method. The decay energies and intrinsic widths of a number of states were measured, and the momentum correlations of three-body decaying states were considered. A second 2p-decaying 2 + state of 12 O was observed for the first time, and a higher energy 12 O state was observed in the 4p+2α decay channel. This 4p+2α channel also contains contributions from fission-like decay paths, including 6 Beg.s.+ 6 Beg.s.. Analogs to these states in 12 O were found in 12 N in the 2p+ 10 B and 2p+α+ 6 Li channels. The momentum correlations for the prompt 2p decay of 12 Og.s. were found to be nearly identical to those of 16 Neg.s., and the correlations for the new 2 + state were found to be consistent with sequential decay through excited states in 11 N. The momentum correlations for the 2 + 1 state in 12 O provide a new value for the 11 N ground-state energy. The states in 12 N/ 12 O that belong to the A=12 isobaric sextet do not deviate from the quadratic isobaric multiplet mass equation (IMME) form.