Single-particle and collective motion in unbound deformed 39Mg

Background: Deformed neutron-rich magnesium isotopes constitute a fascinating territory where the interplay between collective rotation and single-particle motion is strongly affected by the neutron continuum. The unbound fp-shell nucleus Mg-39 is an ideal candidate to study this interplay. Purpose: In this work, we predict the properties of low-lying resonant states of Mg-39, using a suite of realistic theoretical approaches rooted in the open quantum system framework. Method: To describe the spectrum and decay modes of Mg-39 we use the conventional shell model, Gamow shell model, resonating group method, density matrix renormalization group method, and the nonadiabatic particle-plus-rotor model formulated in the Berggren basis. Results: The unbound ground state of Mg-39 is predicted to be either a J(pi) = 7/2(-) state or a 3/2(-) state. A narrow J(pi) = 7/2(-) ground-state candidate exhibits a resonant structure reminiscent of that of its one-neutron halo neighbor Mg-37, which is dominated by the f(7/2) partial wave at short distances and a p(3/2) component at large distances. A J(pi) = 3/2(-) ground-state candidate is favored by the large deformation of the system. It can be associated with the 1/2(-)[321] Nilsson orbital dominated by the l = 1 wave; hence its predicted width is large. The excited J(pi) = 1/2(-) and 5/2(-) states are expected to be broad resonances, while the J(pi) = 9/2(-) and 11/2(-) members of the ground-state rotational band are predicted to have very small neutron decay widths. Conclusion: We demonstrate that the subtle interplay between deformation, shell structure, and continuum coupling can result in a variety of excitations in an unbound nucleus just outside the neutron drip line.