Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for the quasiparticle random-phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probing collective excitations of weakly bound nuclei embedded in the continuum. The monopole excitation modes in magnesium isotopes up to the neutron drip line have been studied with the FAM-QRPA framework on both the coordinate-space and harmonic oscillator basis methods. Enhanced soft monopole strengths and collectivity as a result of weak-binding effects have been unambiguously demonstrated. Nuclei close to the particle drip lines are weakly bound superfluid quantum systems and can exhibit exotic threshold phenomena [1], sharing interdisciplinary interests with weakly bound systems such as multiquark states, Rydberg atoms, and quantum droplets [1][2][3]. Since the discovery of nuclear halos with radioactive beams [4], there have been numerous theo retical developments aiming at weakly bound nuclei and their dilute surfaces [5], Extensive Hartree-Fock-Bogoliubov (HFB) studies have provided successful descriptions of continuum couplings and halo features in ground states of weakly bound nuclei [6][7][8][9][10][11][12]. On the other hand, excitations in weakly bound nuclei opened vast possibilities to probing novel collective modes, as well as continuum effects and components of the effective interaction that are suppressed in ground states [13][14][15], To address these issues, along with the operation of forthcoming facilities such as the Facility for Rare Isotope Beams (FRIB) at Michigan State University, an accurate and self-consistent treatment of continuum together with pairing correlations, deformations, and large spatial extensions is essential.Among the excited states in weakly bound nuclei, the emergent soft excitation modes (or pygmy resonances) which correspond to the collective motion between neutron halo/skins and cores are particularly intriguing. These modes can impact astrophysical neutron capture rates and r-process nucleosynthesis. However, the collectivity of observed pygmy resonances, as a crucial verification of coherence, is still under debate [13,14,16], This Rapid Communication is devoted to the low-energy monopole excitations in weakly bound nuclei caused by the soft incompressibility of halos, as the dilute nuclear matter has a decreased incompressibility compared to saturated densities [17], The low-energy monopole modes indeed have been predicted, e.g., in the neutron-rich nickel isotopes (observed very recently in 68Ni [ 18]), as a rather non collective excitation [19]; however, it may hardly be expected in another random-phase approximation (RPA) calculation with a proper treatment of continuum [20]. Besides, the collectivity could be enhanced due to weak-binding effects [15], Therefore, the emergence of collective soft monopole modes, as well as the role of continuum contributions with the fully self-consistent continuum quasiparticle randomphase approximati...

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.

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.

We have studied odd-even nuclear mass staggering with the Skyrme-Hartree-Fock-Bogoliubov theory by employing isoscalar and isovector contact pairing interactions. By reproducing the empirical odd-even mass differences of the Sn isotopic chain, the strengths of pairing interactions are determined. The optimal strengths adjusted in this work can give better description of oddeven mass differences than that fitted by reproducing the experimental neutron pairing gap of 120 Sn.

8 pages, 10 figures, submitted to PRCInternational audienceUsing the $\hbar$-expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including density-dependent effective mass and spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems