Generalized model screening potentials for Fermi-Dirac plasmas

Abstract

In this paper, some properties of relativistically degenerate quantum plasmas, such as static ion screening, structure factor, and Thomson scattering cross-section, are studied in the framework of linearized quantum hydrodynamic theory with the newly proposed kinetic γ-correction to Bohm term in low frequency limit. It is found that the correction has a significant effect on the properties of quantum plasmas in all density regimes, ranging from solid-density up to that of white dwarf stars. It is also found that Shukla-Eliasson attractive force exists up to a few times the density of metals, and the ionic correlations are seemingly apparent in the radial distribution function signature. Simplified statically screened attractive and repulsive potentials are presented for zero-temperature Fermi-Dirac plasmas, valid for a wide range of quantum plasma number-density and atomic number values. Moreover, it is observed that crystallization of white dwarfs beyond a critical core number-density persists with this new kinetic correction, but it is shifted to a much higher number-density value of n0 ≃ 1.94 × 1037 cm−3 (1.77 × 1010 gr cm−3), which is nearly four orders of magnitude less than the nuclear density. It is found that the maximal Thomson scattering with the γ-corrected structure factor is a remarkable property of white dwarf stars. However, with the new γ-correction, the maximal scattering shifts to the spectrum region between hard X-ray and low-energy gamma-rays. White dwarfs composed of higher atomic-number ions are observed to maximally Thomson-scatter at slightly higher wavelengths, i.e., they maximally scatter slightly low-energy photons in the presence of correction.