Evolution of surface deformations of weakly bound nuclei in the continuum

We study weakly bound deformed nuclei based on the coordinate-space Skyrme Hartree-Fock-Bogoliubov (HFB) approach, in which a large box is employed for treating the continuum and large spatial extensions. When the limit of the core-halo deformation decoupling is approached, calculations found an exotic “egg”-like structure consisting of a spherical core plus a prolate halo in ${}^{38}$Ne, in which the near-threshold nonresonant continuum plays an essential role. Generally the halo probability and the decoupling effect in heavy nuclei can be hindered by high level densities around Fermi surfaces. However, deformed halos in medium-mass nuclei are possible as the negative-parity levels are sparse, e.g., in ${}^{110}$Ge. The deformation decoupling has also been demonstrated in pairing density distributions.

Figure 1

The density profiles of ${}^{38}$Ne, ${}^{40,44}$Mg, ${}^{110}$Ge, and ${}^{224}$Er, which are obtained from calculations with the surface pairing. The density distributions are displayed along the cylindrical coordinates $z$ axis and $r$ axis, respectively. The dashed lines show the density distributions contributed by near-threshold qp continuum states with energies below 1.5 MeV.

Figure 2

The two-dimensional distributions of the neutron density (a) and neutron pairing density (b) in ${}^{38}$Ne, which are displayed on the logarithm scale. The shapes of the core and halo are denoted by dashed lines. Assuming the core has a radius of 9.5 fm, the integrated neutron number inside the core is 26.1; in other words, there are about two neutrons in the halo.

Figure 3

The smoothed occupation numbers of ${\Omega }^{\pi }=1/2^{\pm }$ neutron qp states of ${}^{38}$Ne, ${}^{40}$Mg, and ${}^{44}$Mg. The solid lines and dashed lines show the results with box sizes of 30 and 27 fm, respectively. The continuum thresholds $-{\lambda }_n$ are given, where ${\lambda }_n$ is the neutron Fermi surface energy.

Figure 4

Similar to Fig. 3 but for Ge and Er isotopes. The Nilsson labels are given for near-threshold ${\Omega }^{\pi }=1/2^{-}$ qp states. The arrows in panels are given for guiding eyes for the evolution of phase space decouplings. See text for details.

Figure 5

Quadrupole deformations of neutrons (${\beta }_2^{\mathrm{n}}$, dashed lines), neutron pairing densities (${\beta }_2^{\mathrm{n}-\mathrm{pair}}$, solid lines), proton pairing densities (${\beta }_2^{\mathrm{p}-\mathrm{pair}}$, short-dashed lines), and isovector deformations (${\beta }_2^{\mathrm{n}}-{\beta }_2^{\mathrm{p}}$, thick solid lines) in Ge and Er isotopes. Results are obtained with the surface pairing (the upper panel) and the mixed pairing (the lower panel) interactions, respectively.