A perturbation theory for equation of state of hydrogen in warm and hot dense regimes

In the warm dense regime of hydrogen plasma where the ions and the electrons are strongly coupled, few theoretical models for equation of state (EOS) exist which are accurate enough and simple to implement. In the recent past, we have developed a method for calculating the Helmholtz free energy of a mixture of ions and electrons by combining the orbital-free quantum hypernetted chain (QHNC) method with perturbation theory treating the electron-ion interaction as a perturbation over a reference system of one component plasma (OCP) and uniform electron gas (UEG). However, it was assumed that electrons were at zero Kelvin and a crude formula for the free energy of the UEG was used. This limited the applicability of the method to a small density-temperature regime. In the present work, a finite temperature extension to the orbital-free QHNC theory is derived and is employed in the perturbation theory we developed. Also, an accurate formula given by Ichimaru is used for the free energy of the UEG. EOS, ionic, and electronic structures of fully ionized hydrogen plasma are obtained using the improved method for a wide range of densities and temperatures in the warm and hot dense plasma regimes. The results of the present method are in excellent agreement with those of simulation data for pressures above 1Mbar. It is observed that, above 5 eV, the reference system, i.e., the OCP+UEG, gives the most dominant contribution to EOS and the contribution of perturbation terms is limited to 5%. Published by AIP Publishing.