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Register a new userDeformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations
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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.
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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.
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 systems 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.
A deformed relativistic Hartree-Bogoliubov (DRHB) model is developed aiming at a proper description of exotic nuclei, particularly deformed ones with large spatial extension. In order to give an adequate description of both the contribution of the continuum and the large spatial distribution in exotic nuclei, the DRHB equations are solved in a Woods-Saxon basis in which the radial wave functions have proper asymptotic behaviors at large distance from the nuclear center which is crucial for the formation of halo. The formalism and the numerical procedure of the DRHB model in a Woods-Saxon basis are briefly presented.
In order to study structure of proto-neutron stars and those in subsequent cooling stages, it is of great interest to calculate inhomogeneous hot and cold nuclear matter in a variety of phases. The finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) theory is a primary choice for this purpose, however, its numerical calculation for superfluid (superconducting) many-fermion systems in three dimensions requires enormous computational costs. To study a variety of phases in the crust of hot and cold neutron stars, we propose an efficient method to perform the FT-HFB calculation with the three-dimensional (3D) coordinate-space representation. Recently, an efficient method based on the contour integral of Greens function with the shifted conjugate-orthogonal conjugate-gradient method has been proposed [Phys. Rev. C 95, 044302 (2017)]. We extend the method to the finite temperature, using the shifted conjugate-orthogonal conjugate-residual method. We benchmark the 3D coordinate-space solver of the FT-HFB calculation for hot isolated nuclei and fcc phase in the inner crust of neutron stars at finite temperature. The computational performance of the present method is demonstrated. Different critical temperatures of the quadrupole and the octupole deformations are confirmed for $^{146}$Ba. The robustness of the shape coexistence feature in $^{184}$Hg is examined. For the neutron-star crust, the deformed neutron-rich Se nuclei embedded in the sea of superfluid low-density neutrons appear in the fcc phase at the nucleon density of 0.045 fm$^{-3}$ and the temperature of $k_B T=200$ keV. The efficiency of the developed solver is demonstrated for nuclei and inhomogeneous nuclear matter at finite temperature. It may provide a standard tool for nuclear physics, especially for the structure of the hot and cold neutron-star matters.
We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps $delta_{2n(p)}$. Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond $^{208}$Pb are predicted to be $Z = 120$, $138$ for protons and $N = 172$, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.
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