Hartree-Fock-Bogoliubov descriptions of deformed weakly bound nuclei in large coordinate spaces

Weakly bound deformed nuclei have been studied by the Skyrme Hartree-Fock-Bogoliubov (HFB) approach in large coordinate-space boxes. In particular, the box-size dependence of the HFB calculations of weakly bound deformed nuclei are investigated, including the particle density and pairing density distributions at nuclear surfaces, the near-threshold resonant and continuum quasiparticle spectra, and energetic properties. The box size may have larger influences in pairing properties than in other bulk properties. We demonstrate that large-box calculations of weakly bound nuclei are important to precisely describe exotic phenomena such as deformed halos and peninsulas of stability beyond drip lines.

Figure 1

Neutron density ${\rho }_n$ profiles of ${}^{42}$Mg calculated by HFB-HO, HFB-THO, and HFB-AX. HFB-HO and HFB-THO calculations are based on 30 HO shells and HFB-AX calculations are done within a box of 30 fm. Density distributions are displayed along the cylindrical coordinates, $z$ axis (solid line) and $r$ axis (dashed line), respectively.

Figure 2

Neutron density ${\rho }_n$ and neutron pairing density ${\tilde{\rho }}_n$ profiles of (a) ${}^{34}$Ne, (b) ${}^{36}$Ne, and (c) ${}^{38}$Ne. Density and pairing density distributions are displayed along the cylindrical coordinates $z$ axis (solid line) and $r$ axis (dashed line), respectively.

Figure 3

Neutron density ${\rho }_n$ and neutron pairing density ${\tilde{\rho }}_n$ profiles of (a) ${}^{40}$Mg, (b) ${}^{42}$Mg, and (c) ${}^{44}$Mg. Density $\rho$ and pairing density $\tilde{\rho }$ distributions are displayed along the cylindrical coordinates $z$ axis (solid line) and $r$ axis (dashed line), respectively.

Figure 4

(a) Neutron density ${\rho }_n$ and (b) neutron pairing density ${\tilde{\rho }}_n$ of ${}^{38}$Ne calculated with box sizes of 24, 30, and 36 fm. Density and pairing density distributions are displayed along the cylindrical coordinates $z$ axis (solid line) and $r$ axis (dashed line), respectively.

Figure 5

Smoothed particle occupation numbers of ${\Omega }^{\pi }=1/2^{\pm }$ neutron quasiparticle states of ${}^{42}$Mg. Quasiparticle spectra obtained by (a) HFB-HO and (b) HFB-THO with 30 shells on the HO/THO basis and by HFB-AX (solid line) with a box size of 30 fm.

Figure 6

Smoothed particle occupation numbers of ${\Omega }^{\pi }=1/2^{\pm }$ neutron quasiparticle states of ${}^{38}$Ne obtained by HFB-AX with box sizes of (a) 24 fm, (b) 30 fm, and (c) 36 fm. The continuum thresholds, i.e., $-{\lambda }_n$, are given, where ${\lambda }_n$ is the neutron Fermi energy.

Figure 7

Smoothed pairing occupation numbers of ${\Omega }^{\pi }=1/2^{\pm }$ neutron quasiparticle states of ${}^{38}$Ne obtained by HFB-AX with box sizes of (a) 24 fm, (b) 30 fm, and (c) 36 fm. Continuum thresholds, $-{\lambda }_n$, are given, where ${\lambda }_n$ is the neutron Fermi energy.

Figure 8

Neutron Fermi energies of Nd isotopes calculated by HFB-THO (with 30 shells of THO basis) and HFB-AX (with a 30-fm box).