Electrostatic energy of Coulomb crystals with polarized electron background

Abstract

Outer crusts of neutron stars and interiors of cool white dwarfs consist of bare atomic nuclei, arranged in a crystal lattice and immersed in a Fermi gas of degenerate electrons. We study electrostatic properties of such Coulomb crystals, taking into account the polarizability of the electron gas and considering different lattice structures, which can form the ground state. To take the electron background polarization into account, we use the linear response theory with the electron dielectric function given either by the Thomas-Fermi approximation or by the random-phase approximation (RPA). We compare the widely used nonrelativistic (Lindhard) version of the RPA approximation with the more general, relativistic (Jancovici) version. The results of the different approximations are compared to assess the importance of going beyond the Thomas-Fermi or Lindhard approximations. We also include contribution of zero-point vibrations of ions into the ground-state energy. We show that the bcc lattice forms the ground state for any charge number $Z$ of the atomic nuclei at the densities where the electrons are relativistic ($\rho \gtrsim 10^6$ g cm${}^{-3}$), while at lower densities the fcc and hcp lattices can form the ground state. The MgB${}_2$-like lattice never forms the ground state at realistic densities in the crystallized regions of degenerate stars. The RPA corrections strongly affect the boundaries between the phases. As a result, transitions between different ground-state structures depend on $Z$ in a nontrivial way. The relativistic and quantum corrections produce less dramatic effects, moderately shifting the phase boundaries.

10 pages, 5 figures

References in corpus (9)

• Classical and quantum Coulomb crystals
• Electron-ion scattering in dense multi-component plasmas: application to the outer crust of an accreting neutron star
• Magnetic-field evolution in a plastically-failing neutron-star crust
• Binary and ternary ionic compounds in the outer crust of a cold nonaccreting neutron star
• Correlation effects in partially ionized mass asymmetric electron-hole plasmas
• Electron exchange and polarization effects on electron captures and neutron emissions by nuclei in white dwarfs and neutron stars
• Deformed crystals and torsional oscillations of neutron star crust
• Electrostatic energy and phonon properties of Yukawa crystals
• Properties of magnetized Coulomb crystals of ions with polarizable electron background

Cited by in corpus (2)

• Current challenges in the physics of white dwarf stars
• Elastic properties of Yukawa crystals