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Accurate Diffusion Coefficients for Dense White Dwarf Plasma Mixtures

Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate at weak coupling ($Γ\ll 1$), but they have errors as large as a factor of two in the strongly coupled liquid regime ($1 \lesssim Γ\lesssim 200$). With modern molecular dynamics codes it is possible to accurately determine diffusion coefficients in select systems with percent-level precision. In this work, we develop a theoretically motivated law for diffusion coefficients which works across the wide range of parameters typical for white dwarf interiors. We perform molecular dynamics simulations of pure systems and two mixtures that respectively model a typical-mass C/O white dwarf and a higher-mass O/Ne white dwarf, and resolve diffusion coefficients for several trace neutron-rich nuclides. We fit the model to the pure systems and propose a physically motivated generalization for mixtures. We show that this model is accurate to roughly 15% when compared to molecular dynamics for many individual elements under conditions typical of white dwarfs, and is straightforward to implement in stellar evolution codes.