Role of quadrupole deformation and continuum effects in the “island of inversion” nuclei F28,29,31

Abstract

Background: The peculiar properties of nuclei in the so-called ``island of inversion'' around $Z=10$ and $N=20$ are the focus of current nuclear physics research. Recent studies showed that $^{28}\mathrm{F}$ has a negative-parity ground state and thus lies within the southern shore of the island of inversion, and $^{29}\mathrm{F}$ presents a halo structure in its ground state, but it is unclear which effects, such as deformation, shell evolution due to tensor forces, or couplings to the continuum, lead to this situation.Purpose: We investigate the role of quadrupole deformation and continuum effects on the single-particle structure of $^{28,29,31}\mathrm{F}$ from a relativistic mean-field approach and show how both phenomena can lead to a negative-parity ground state in $^{28}\mathrm{F}$ and halo structures in $^{29,31}\mathrm{F}$.Methods: We solve the Dirac equation in the complex-momentum (Berggren) representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field calculations using the NL3 interaction and calculate the continuum level densities using the Green's function method.Results: We extract single-particle energies and widths from the continuum level densities to construct the Nilsson diagrams of $^{28,29,31}\mathrm{F}$ in the continuum and analyze the evolution of both the widths and occupation probabilities of relevant Nilsson orbitals in $^{28}\mathrm{F}$ and find that some amount of prolate deformation must be present. In addition, we calculate the density distributions for bound Nilsson orbitals near the Fermi surface in $^{29,31}\mathrm{F}$ and reveal that, for a quadrupole deformation $0.3\ensuremath{\le}{\ensuremath{\beta}}_{2}\ensuremath{\le}0.45$ (prolate), characteristic halo tails appear at large distances.Conclusions: Using the relativistic mean-field approach in the complex-momentum representation with the Green's function method, we demonstrate that in neutron-rich fluorine isotopes, while in the spherical case the $pf$ shells are already inverted and close to the neutron emission threshold, a small amount of quadrupole deformation can dramatically reduce the gap between positive- and negative-parity states and increase the role of continuum states, ultimately leading to the negative parity in the ground state of $^{28}\mathrm{F}$ and the halo structures in $^{29,31}\mathrm{F}$.