  We study the contribution of electron-atom interaction to the equation of
state for partially ionized hydrogen plasma using the cluster-virial expansion.
For the first time, we use the Beth-Uhlenbeck approach to calculate the second
virial coefficient for the electron-atom (bound cluster) pair from the
corresponding scattering phase-shifts and binding energies. Experimental
scattering cross-sections as well as phase-shifts calculated on the basis of
different pseudopotential models are used as an input for the Beth-Uhlenbeck
formula. By including Pauli blocking and screening in the phase-shift
calculation, we generalize the cluster-virial expansion in order to cover also
near solid density plasmas. We present results for the electron-atom
contribution to the virial expansion and the corresponding equation of state,
i.e. pressure, composition, and chemical potential as a function of density and
temperature. These results are compared with semi-empirical approaches to the
thermodynamics of partially ionized plasmas. Avoiding any ill-founded input
quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom
interaction represents a benchmark for other, semi-empirical approaches.
