Average atom models are inexpensive but reasonably accurate models used for calculating the material properties of dense plasmas.
The Tartarus average atom model approximates a material by an ensemble of identical average atoms.
Each atom is confined to a sphere, whose radius -- the ion-sphere radius -- is determined by the mass density and atomic mass of the element.
At the boundary of the sphere, it is assumed that the interaction potential between the electrons and the plasma goes to a constant -- the muffin-tin constant.
Inside the spheres, density function theory is used to find the electronic structure, and the boundary condition at the edge of the sphere is assumed to be a free-electron behavior.
This is the Inferno model, first described by Liberman in 1979. It has proved difficult to make a numerically robust implementation of this model that works 'everywhere'.
The unique innovation of the Tartarus model is to use complex contour integration for energy integrals. This is possible due to the use of the Green's function representation (as opposed to using orbitals).
The code is fast and stable (but not perfect!).
The algorithm and equations of the model are described in the Tartarus main paper. The idea was first introduced in this article, published in Science Direct, and the relativistic version worked out in this issue of High Energy Density Physics.
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