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

TL;DR

This paper calculates second Born corrections to electrical and thermal conductivities in dense liquid metal matter, providing a semi-analytical approach that improves accuracy and Z-dependence understanding for astrophysical applications.

Contribution

It introduces a semi-analytical method for calculating second Born corrections, enhancing accuracy and Z-dependence analysis compared to previous numerical approaches.

Findings

Second Born corrections are sufficient for Z<26.

The semi-analytical approach matches previous numerical results.

Results are provided as practical analytic formulas.

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 \rho-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 results are parameterized in a form of analytic formulae that would facilitate practical uses of the results. We also extend our calculations to the case of mixtures of nuclear species. The corresponding subroutine can be retrieved from http://www.ph.sophia.ac.jp/~itoh-ken/subroutine/subroutine.htm