Ion Structure Factors and Electron Transport in Dense Coulomb Plasmas

Abstract

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...

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