Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus

Abstract

ABSTRACT The main contribution to the effective shear modulus of neutron star crust can be calculated within Coulomb solid model and can be approximated by simple analytical expression for arbitrary (even multicomponent) composition. Here I consider correction associated with electron screening within Thomas–Fermi approximation. In particular, I demonstrate that for relativistic electrons (density ρ > 106 g cm−3) this correction can be estimated as $\delta \mu _\mathrm{eff}^\mathrm{V}= -9.4\times 10^{-4}\sum _Z n_Z Z^{7/3} e^2/a_\mathrm{e},$ where summation is taken over ion species, nZ is number density of ions with charge Ze, kTF is Thomas–Fermi screening wavenumber. Finally, ae = (4πne/3)−1/3 is electron sphere radius. Quasi-neutrality condition ne = ∑ZZnZ is assumed. This result holds true for arbitrary (even multicomponent and amorphous) matter and can be applied for neutron star crust and (dense) cores of white dwarfs. For example, the screening correction reduces shear modulus by ∼9 per cent for Z ∼ 40, which is typical for inner layers of neutron star crust.