Fully self-consistent band calculation has been performed for slab phase in neutron-star inner crust, using the BCPM energy density functional. Optimized slab structure is calculated at given baryon density either with the fixed proton ratio or with the beta-equilibrium condition. Numerical results indicate the band gap of in order of keV to tens of keV, and the mobility of dripped neutrons are enhanced by the Bragg scattering, which leads to the macroscopic effective mass,m * z /mn = 0.65 ∼ 0.75 near the bottom of the inner crust in neutron stars. We also compare the results of the band calculation with those of the Thomas-Fermi approximation. The Thomas-Fermi approximation becomes invalid at low density with high proton ratio.

Background: 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. 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) coordinatespace representation. Methods: Recently, an efficient method based on the contour integral of Green's 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 conjugateorthogonal 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 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 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 the hot and cold neutron-star matters.

We present recent results in theoretical studies on nuclear structure and reaction beyond mean field, using the adiabatic self-consistent collective coordinate method and its extension. We also present new results with the finite-temperature Hartree-Fock-Bogoliubov calculation with the threedimensional-coordinate-space representation.

The pasta phases of nuclear matter, whose existence is suggested at low density, may influence observable properties of neutron stars. In order to investigate properties of the neutron star matter, we calculate self-consistent solutions for the ground states of slab-like phase using the microscopic density functional theory with Bloch wave functions. The calculations are performed at each point of fixed average density and proton fraction (ρ, Y p ), varying the lattice constant of the unit cell. For small Y p values, the dripped neutrons emerge in the ground state, while the protons constitute the slab (crystallized) structure. The shell effect of protons affects the thickness of the slab nuclei.