Equation of state of dense plasmas of mixture. Application to the center of the sun

Complete text of publication follows. We present a quantum-statistical model for the calculation of atomic structure and equation of state of mixture plasmas (i.e. plasmas containing different elements). An ion of charge q+ is defined as the ensemble of configurations having (Z-q) bound electrons. When the number of configurations becomes too large, they can be gathered into super-configurations. In each (super-) configuration, the nucleus is totally screened by the electrons (spherical symmetry of the central-field model). Bound and free electrons are described within a quantum-mechanical self-consistent procedure and relativistic effects are taken into account in the Pauli approximation. The assumption that all the ionic species of all the elements should have the same electronic environment leads to the equality of electronic pressure for all ions having therefore different volumes. The partial volumes are therefore obtained from the equality of the electronic pressure, evaluated by the stress-tensor formula, for all the (super-) configurations. The thermodynamic consistency resulting from this 'redefinition' of ions is the most important feature of the method. The numerical procedure is particularly robust, and can handle plasmas where light and heavy nuclei co-exist. The present study shows that the atomic radius of a particular element in the mixture is modified by the atomic shell structure of the other elements (i.e. by the fact that the ionization potentials differ from an element to another). With such a proper treatment of the interactions between electrons and between electron and nucleus, this model can produce reliable stellar opacities and equations of state. Calculations of the pressure in the center of the Sun will be presented, and compared with other models.