Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for quasiparticle random phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probe collective excitation
s 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.
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, incl
uding 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.
The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi system
s with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.
The coordinate space formulation of the Hartree-Fock-Bogoliubov (HFB) method enables self-consistent treatment of mean-field and pairing in weakly bound systems whose properties are affected by the particle continuum space. Of particular interest are
neutron-rich, deformed drip-line nuclei which can exhibit novel properties associated with neutron skin. To describe such systems theoretically, we developed an accurate 2D lattice Skyrme-HFB solver {hfbax} based on B-splines. Compared to previous implementations, we made a number of improvements aimed at boosting the solvers performance. These include: explicit imposition of axiality and space inversion, use of the modified Broydens method to solve self-consistent equations, and a partial parallelization of the code. {hfbax} has been benchmarked against other HFB solvers, both spherical and deformed, and the accuracy of the B-spline expansion was tested by employing the multiresolution wavelet method. Illustrative calculations are carried out for stable and weakly bound nuclei at spherical and very deformed shapes, including constrained fission pathways. In addition to providing new physics insights, {hfbax} can serve as a useful tool to assess the reliability and applicability of coordinate-space and configuration-space HFB solvers, both existing and in development.
