Continuous free-electron state-density modeling based on plasma microfield

Following the atomic model based on the microfield in a plasma for bound states [Astrophysical Journal 532, 670 (2000)], I have considered an atomic modeling for computing the free-electron state-density based on the plasma microfield. In the atomic model based on the plasma microfield, it is considered that an ion in plasma is immersed in a uniform electric field that is the contribution of field values averaged over the other ions in the plasma. It has been expected a modeling for the free-state density consistent with its bound state, because the resulting free-state densities by the simple atomic model based on the plasma microfield has been found to be invalid. In this study, I have obtained a physically appropriate free-state density under the assumption that the large electric field component can be considered to exist due to the electric field originating from the nearest neighboring ion and the resulting potential around the ion shows mirror symmetry about the saddle point. The resulting state density is consistent with the experimental results. The inclusion of the free-state density has caused a slight deviation in the values of the average ionization degree of hydrogenic plasmas