Coordinate-space solver for finite-temperature Hartree-Fock-Bogoliubov calculations using the shifted Krylov method

概要

Background: In order to study structure of protoneutron 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.

Purpose: 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.

Methods: Recently, an efficient method based on the contour integral of Green's function with the shifted conjugate-orthogonal conjugate-gradient method was proposed [Phys. Rev. C 95, 044302 (2017)]. We extend the method to finite temperature, using the shifted conjugate-orthogonal conjugate-residual method.

Results: 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 146Ba. The robustness of the shape coexistence feature in 184Hg is examined. For the neutron-star crust, deformed neutron-rich Se nuclei embedded in the sea of superfluid low-density neutrons appear in the fcc phase at a nucleon density of 0.045 fm?3 and a temperature of kBT=200 keV.

Conclusions: 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 hot and cold neutron-star matter.