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 structures, which can form the ground state: body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal close-packed (hcp), and MgB_{2}-like lattices. At zero temperature the electrostatic energy provides a fundamental contribution to the total energy of the classical Coulomb crystal, which allows us to study structural transitions in the neutron-star crusts and crystallized white-dwarf interiors. 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 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 the 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 (ρâ³10^{6}g cm^{-3}), while at the nonrelativistic densities (ρâ²10^{6}g cm^{-3}) 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.
ABSTRACT
Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [A. Y. Potekhin, G. Chabrier, and F. J. Rogers, Phys. Rev. E 79, 016411 (2009)], which covers the transition between the weak and strong Coulomb coupling regimes and reproduces numerical results obtained in the hypernetted-chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong-coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes post-Debye density corrections to the case of mixtures and numerically agrees with the HNC approximation in that regime.
Subject(s)
Algorithms , Complex Mixtures/chemistry , Gases/chemistry , Hot Temperature , Models, Chemical , Rheology/methods , Static Electricity , Computer SimulationABSTRACT
Phonon frequency moments and thermodynamic functions (electrostatic and vibrational parts of the free energy, internal energy, and heat capacity) are calculated for bcc and fcc Coulomb crystals in the harmonic approximation with a fractional accuracy < or equivalent to 10(-5). Temperature dependence of thermodynamic functions is fitted by analytical formulas with an accuracy of a few parts in 10(5). The static-lattice (Madelung) part of the free energy is calculated with an accuracy of approximately 10(-12). The Madelung constant and frequency moments of hcp crystals are also computed.
ABSTRACT
We study the thermodynamic properties of a partially ionized hydrogen plasma in strong magnetic fields, B approximately 10(12)-10(13) G, typical of neutron stars. The properties of the plasma depend significantly on the quantum-mechanical sizes and binding energies of the atoms, which are strongly modified by thermal motion across the field. We use new fitting formulas for the atomic binding energies and sizes, based on accurate numerical calculations and valid for any state of motion of the atom. In particular, we take into account decentered atomic states, neglected in previous studies of thermodynamics of magnetized plasmas. We also employ analytic fits for the thermodynamic functions of nonideal fully ionized electron-ion Coulomb plasmas. This enables us to construct an analytic model of the free energy. An ionization equilibrium equation is derived, taking into account the strong magnetic field effects and the nonideality effects. This equation is solved by an iteration technique. Ionization degrees, occupancies, and the equation of state are calculated.
