Abstract. The diffusive thermal conductivity of neutrons in dense matter [ρ ∼ (1−8)×1014 g cm −3 ] of neutron star cores is calculated. The contribution from neutron-neutron and neutron-proton collisions is taken into account. We use the transition probabilities calculated for symmetric dense nucleon matter on the basis of the DiracBrueckner approach to the in-medium effects and the Bonn model of bare nucleon-nucleon interaction. The diffusive thermal conductivity of neutrons in the presence of neutron and proton superfluidities is analyzed in a microscopic manner; the effects of superfluidity are shown to be significant. The low temperature behavior of the thermal conductivity appears to be extremely sensitive to the relation between critical temperatures of neutrons and protons. The results are fitted by simple analytic expressions. In combination with the formulae for the electron and muon thermal conductivities, obtained earlier, the present expressions provide a realistic description of the full diffusive thermal conductivity in the neutron star cores for normal and various superfluid phases.
The dynamical structure factor of a Coulomb crystal of ions is calculated at arbitrary temperature below the melting point, taking into account multiphonon processes in the harmonic approximation. In a strongly coupled Coulomb ion liquid, the static structure factor is split into two parts, a Braggdiffraction-like one, describing incipient long-range order structures, and an inelastic part corresponding to thermal ion-density fluctuations. It is assumed that the diffractionlike scattering does not lead to the electron relaxation in the liquid phase. This assumption, together with the inclusion of multiphonon processes in the crystalline phase, eliminates large discontinuities of the transport coefficients ( jumps of the thermal and electric conductivities, as well as shear viscosity, reported previously) at a melting point.[ S0031-9007(98)07942-3] PACS numbers: 52.25.Fi, 95.30.Qd, 97.20.Rp, 97.60.JdWe consider a strongly coupled Coulomb plasma (SCCP) of ions immersed in a nearly uniform chargecompensating electron gas. The ions may be disordered (liquid phase) or arranged in a crystalline lattice. The energetically favorable body-centered cubic (bcc) lattice appears at G . G m ഠ 172 [1], where G ͑Ze͒ 2 ͞aT is the ion-coupling parameter, T is the temperature, a ͑4pn i ͞3͒ 21͞3 , and n i is the ion number density.Many astrophysical objects (interiors of white dwarfs, massive stars, and giant planets; envelopes of neutron stars) are made of such a plasma. Its kinetic properties required for various applications are determined mainly by electron-ion (ei) scattering. A general framework for calculation of these transport properties has been described in [2]. Numerous calculations (e.g., [3][4][5][6][7]), done under additional assumption of strong electron degeneracy, predict large (a factor of 3-4) discontinuities of the electric and thermal conductivities at the melting point. In contrast, the thermodynamic quantities in the liquid and solid phases, determined solely by ions, are very similar near G G m (e.g., [1,8]). This suggests that properties of the ion system serving as a main scatterer for electrons should vary smoothly through the melting transition. In this Letter, we propose a modification of the transport theory which removes large jumps of the transport coefficients.The differential ei scattering rate in a SCCP averaged over initial and summed over final electron spin states s and s 0 iswhere N is the total number of ions, p and p 0 are the electron momenta before and after scattering, respectively, hq p 0 2 p,hv e 0 2 e is the difference between final and initial electron energies, and U q,s 0 s is the matrix element of the operator of elementary ei interaction. S ͑q, v͒ is the dynamical structure factor of the plasma, the most important quantity of the theory. In the liquid regime,r͑x, t͒ is the operator of the charge density in units of Zjej:r͑x, t͒ n I ͑x, t͒ 2 n i , wheren I ͑x, t͒ is the ion-density operator and n i n e ͞Z takes account of the compensating electron background with the electron densi...
The strength of neutron star crust is crucial for modelling magnetar flares, pulsar glitches and gravitational wave emission. We aim to shed some light on this problem by analysing uniaxial stretch deformation (elongation and contraction) of perfect bodycentered cubic Coulomb crystals, paying special attention to the inherent anisotropy of this process. Our analysis is based on the semi-analytical approach of Baiko & Kozhberov (2017), which, for any uniform deformation, allows one to calculate, in fully non-linear regime, critical deformation parameters beyond which the lattice loses its dynamic stability. We determine critical strain, pressure anisotropy and deformation energy for any stretch direction with respect to the crystallographic axes. These quantities are shown to be strongly anisotropic: they vary by a factor of almost 10 depending on the orientation of the deformation axis. For polycrystalline crust, we argue that the maximum strain for the stretch deformation sustainable elastically is 0.04. It is lower than the breaking strain of 0.1 obtained in molecular dynamic simulations of a shear deformation by Horowitz & Kadau (2009). The maximum pressure anisotropy of polycrystalline matter is estimated to be in the range from 0.005 to 0.014 nZ 2 e 2 /a, where n is the ion number density, Ze is the ion charge, and a is the ion-sphere radius. We discuss possible mechanisms of plastic motion and formation of large crystallites in neutron star crust as well as analyse energy release associated with breaking of such crystallites in the context of magnetic field evolution and magnetar flaring activity.
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.
The body-centered-cubic Coulomb crystal of ions in the presence of a uniform magnetic field is studied using the rigid electron background approximation. The phonon mode spectra are calculated for a wide range of magnetic-field strengths and for several orientations of the field in the crystal. The phonon spectra are used to calculate the phonon contribution to the crystal energy, entropy, specific heat, Debye-Waller factor of ions, and the rms ion displacements from the lattice nodes for a broad range of densities, temperatures, chemical compositions, and magnetic fields. Strong magnetic field dramatically alters the properties of quantum crystals. The phonon specific heat increases by many orders of magnitude. The ion displacements from their equilibrium positions become strongly anisotropic. The results can be relevant for dusty plasmas, ion plasmas in Penning traps, and especially for the crust of magnetars (neutron stars with superstrong magnetic fields B > or approximately equal 10(14) G ). The effect of the magnetic field on ion displacements in a strongly magnetized neutron star crust can suppress the nuclear reaction rates and make them extremely sensitive to the magnetic-field direction.
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