The Second Born Corrections to the Electrical and Thermal Conductivities of Dense Matter in the Liquid Metal Phase

Abstract

The second Born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. Inclusion up to the second Born corrections is sufficiently accurate for the Coulomb scattering of the electrons by the atomic nuclei with Z 26. Our approach is semi-analytical, and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the Coulomb scattering of the electron by the atomic nucleus. The merit of the present semi-analytical approach is that this approach affords us to obtain the results with reliable Z-dependence and ρ-dependence. The previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of Z-values, Z=6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0.05MeV, 0.1MeV, 0.2MeV, 0.4MeV, 0.7MeV, 1MeV, 2MeV, 4MeV, and 10MeV. Our study, however, has confirmed that the previous results are sufficiently accurate. They are recovered, if the terms higher than the second Born terms are taken into account. We make a detailed comparison of the present results with those of the previous authors. The numerical

New parsec data base of α-enhanced stellar evolutionary tracks and isochrones – I. Calibration with 47 Tuc (NGC 104) and the improvement on RGB bump

“…Suffice it to recall that the Rosseland mean opacities come from two sources: from the Opacity Project At Livermore (OPAL, Iglesias & Rogers 1996, and references therein) 2 team at high temperatures (4.0 < log(T/K) < 8.7), and from AESOPUS (Marigo & Aringer 2009) 3 at low temperatures (3.2 < log(T/K) < 4.1), with a smooth transition being adopted in the 4.0 < log(T/K) < 4.1 interval. Conductive opacities are provided by Itoh et al (2008) routines. As for the EOS, we choose the widely used FreeEOS code (version 2.2.1 in the EOS4 configuration) 4 developed by Alan W. Irwin for its computational efficiency.…”

Red Giant evolution and specific problems

“…Conductive opacities are included following [4]. The nuclear reaction network consists of the p-p chains, the CNO tri-cycle, the Ne-Na and Mg-Al chains, and the most important -capture reactions, including the -n reactions.…”

“…1 H, D, 3 He, 4 He, 7 Li, 8 Be, 4 He, 12 C, 13 C, 14 N, 15 N, 16 N, 17 N, 18 O, 19 F, 20 Ne, 21 Ne, 22 Ne, 23 Na, 24 Mg, 25 Mg, 26 Mg, 26 Al m , 26 Al g , 27 Al, 28 Si. In total we consider 42 reaction rates, that are taken from the recommended rates in the JINA reaclib database [5] from which we also take the corresponding Q-values.…”

Electrical conductivity tensor of dense plasma in magnetic fields

“…These calculations agree with those of Itoh et al [7] who also provide useful fitting formulae for the transport coefficient. Subsequent refinements of the results quoted above included, among other things, multi-phonon process and Debye-Waller factor [8] in the solid phase and improved correlation functions in the liquid phase [9]. The implementation of the transport coefficients of dense matter in the dissipative MHD equations in the case of cold neutron crust plasma in the presence of magnetic fields were discussed by a number of authors [10, 11].…”