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\ncalculated for the dense matter in the liquid metal phase for various elemental\ncompositions of astrophysical importance. Inclusion up to the second Born\ncorrections is sufficiently accurate for the Coulomb scattering of the\nelectrons by the atomic nuclei with Z < 26. Our approach is semi-analytical,\nand is in contrast to that of the previous authors who have used fully\nnumerical values of the cross section for the Coulomb scattering of the\nelectron by the atomic nucleus. The merit of the present semi-analytical\napproach is that this approach affords us to obtain the results with reliable\nZ-dependence and \\rho-dependence. The previous fully numerical approach has\nmade use of the numerical values of the cross section for the scattering of the\nelectron off the atomic nucleus for a limited number of Z-values, Z=6, 13, 29,\n50, 82, and 92, and for a limited number of electron energies, 0.05MeV, 0.1MeV,\n0.2MeV, 0.4MeV, 0.7MeV, 1MeV, 2MeV, 4MeV, and 10MeV. Our study, however, has\nconfirmed that the previous results are sufficiently accurate. They are\nrecovered, if the terms higher than the second Born terms are taken into\naccount. We make a detailed comparison of the present results with those of the\nprevious authors. The numerical results are parameterized in a form of analytic\nformulae that would facilitate practical uses of the results. We also extend\nour calculations to the case of mixtures of nuclear species. The corresponding\nsubroutine can be retrieved from\nhttp://www.ph.sophia.ac.jp/~itoh-ken/subroutine/subroutine.htm\n