# Self-consistent band calculation of slab phase in neutron-star crust

## TL;DR

This study performs a self-consistent band calculation for the slab phase in neutron-star crusts, revealing band gaps, neutron mobility enhancement, and limitations of the Thomas-Fermi approximation at low densities.

## Contribution

It introduces a fully self-consistent band calculation method for neutron-star crust slabs using the BCPM functional, providing new insights into neutron mobility and band gaps.

## Key findings

- Band gaps are in the keV to tens of keV range.
- Neutron mobility is enhanced by Bragg scattering.
- Thomas-Fermi approximation fails at low density with high proton ratio.

## Abstract

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, $\bar{m}^*_z/m_n=0.65\sim 0.75$ 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.