Single-particle and collective motion in unbound deformed ${}^{39}\text{Mg}$

Abstract

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 ${}^{39}\text{Mg}$ is an ideal candidate to study this interplay. Purpose: In this work, we predict the properties of low-lying resonant states of ${}^{39}\text{Mg}$, using a suite of realistic theoretical approaches rooted in the open quantum system framework. Method: To describe the spectrum and decay modes of ${}^{39}\text{Mg}$ we use the conventional Shell Model, Gamow Shell Model, Resonating Group Method, Density Matrix Renormalization Group method, and the non-adiabatic Particle-Plus-Rotor model formulated in the Berggren basis. Results: The unbound ground state of ${}^{39}\text{Mg}$ 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 ${}^{37}\text{Mg}$, 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 $\ell =1$ 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.

9 pages, 6 figures

References in corpus (7)

• Shell Model in the Complex Energy Plane
• A new effective interaction for $0\hslash \omega$ shell model calculations in the sdpf valence space
• Density matrix renormalization group approach for many-body open quantum systems
• Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons
• Density matrix renormalization group approach to two-fluid open many-fermion systems
• Three-body correlations in the ground-state decay of 26O
• One-particle properties of deformed N $\approx$ 28 odd-N nuclei with weakly-bound or resonant neutrons

Cited by in corpus (10)

• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• Quantified Gamow Shell Model interaction for $psd$-shell nuclei
• Ab initio Gamow in-medium similarity renormalization group with resonance and continuum
• Toward Scalable Many-Body Calculations for Nuclear Open Quantum Systems using the Gamow Shell Model
• Description of proton-rich nuclei in the $A\sim 20$ region with the Gamow shell model
• One-neutron halo structure of ${}^{29}$Ne
• Prediction of two-neutron halos in the $N=28$ isotones ${}^{40}$Mg and ${}^{39}$Na
• Weak binding effects on the structure of ${}^{40}$Mg
• Perspectives on few-body cluster structures in exotic nuclei
• Fast rotation of nuclei with extreme isospin in the vicinity of neutron and proton drip lines