Single-particle spectral function for the classical one-component plasma

TL;DR

This paper calculates the spectral function of an electron plasma using a self-consistent GW0 approach, introduces a new analytic solution for the self-energy, and demonstrates its accuracy and usefulness for plasma property calculations.

Contribution

A novel non-perturbative analytic solution for the GW0 self-energy as a function of momentum is presented, improving the calculation of spectral functions in correlated plasmas.

Findings

The analytic solution reproduces numerical spectral data with less than 10% error for certain plasma regimes.

The non-perturbative self-energy scales as n^(1/4) at low densities, unlike perturbative results.

The derived formulas accurately predict the chemical potential shift with less than 10% deviation at relevant plasma conditions.

Abstract

The spectral function for an electron one-component plasma is calculated self-consistently using the GW0 approximation for the single-particle self-energy. In this way, correlation effects which go beyond the mean-field description of the plasma are contained, i.e. the collisional damping of single-particle states, the dynamical screening of the interaction and the appearance of collective plasma modes. Secondly, a novel non-perturbative analytic solution for the on-shell GW0 self-energy as a function of momentum is presented. It reproduces the numerical data for the spectral function with a relative error of less than 10% in the regime where the Debye screening parameter is smaller than the inverse Bohr radius, kappa<1/a_B. In the limit of low density, the non-perturbative self-energy behaves as n^(1/4), whereas a perturbation expansion leads to the unphysical result of a density independent self-energy [W. Fennel and H. P. Wilfer, Ann. Phys. Lpz._32_, 265 (1974)]. The derived expression will greatly facilitate the calculation of observables in correlated plasmas (transport properties, equation of state) that need the spectral function as an input quantity. This is demonstrated for the shift of the chemical potential, which is computed from the analytical formulae and compared to the GW0-result. At a plasma temperature of 100 eV and densities below 10^21 cm^-3, both approaches deviate less than 10% from each other.