A simplified approach to calculate atomic partition functions in plasmas

A simplified method to calculate the electronic partition functions and the corresponding thermodynamic properties of atomic species is presented and applied to C(I) up to C(VI) ions. The method consists in reducing the complex structure of an atom to three lumped levels. The ground level of the lumped model describes the ground term of the real atom, while the second lumped level represents the low lying states and the last one groups all the other atomic levels. It is also shown that for the purpose of thermodynamic function calculation, the energy and the statistical weight of the upper lumped level, describing high-lying excited atomic states, can be satisfactorily approximated by an analytic hydrogenlike formula. The results of the simplified method are in good agreement with those obtained by direct summation over a complete set (i.e., including all possible terms and configurations below a given cutoff energy) of atomic energy levels. The method can be generalized to include more lumped levels in order to improve the accuracy.