Improving conductivity calculations with accurate electron-electron scattering rate predictions*

Magnetohydrodynamic (MHD) simulations are commonly used for modeling inertial confinement fusion (ICF) experiments. These simulations are governed by a set of MHD equations, which rely on transport coefficients, such as the DC electrical conductivity, for closure. In the warm dense matter (WDM) regime, obtaining experimental DC conductivity values is challenging and theoretical models are needed. We use first-principles calculations to study isochorically heated beryllium, a commonly used material in ICF experiments, at densities of 0.80, 1.97, and 3.94 g/cc. In this work we focus on electron-electron (e-e) scattering, a process not captured in DFT studies, which can play a key role in the DC conductivity of a material. To study this scattering process, we take advantage of the relationship between the electronic self-energy, which can be calculated within the GW approximation, and the e-e scattering rate. Using compressed Matsubara-frequency grids, we calculate the electronic self-energies at electronic temperatures between 0.01 and 5.00 eV, resulting in finite-temperature e-e scattering rates. We then compare our results from the computationally expensive GW calculation to scattering rates predicted by Fermi liquid (FL) theory. The FL rates only rely on accessible materials specific parameters, such as the Fermi energy, chemical potential, and the Wigner–Seitz radius. Our comparison between the two methods finds overall good agreement between the GW and FL methods, justifying the use of FL e-e scattering rates to inform DC conductivity values at moderate temperatures in the WDM regime. These results will improve the accuracy and efficiency of DC conductivity predictions, leading to more accurate closure parameters for the MHD simulation equations, thus leading to more accurate ICF modeling.