Cluster virial expansion and electron-hydrogen molecule scattering

The equation of state of partially ionized hydrogen plasma is considered with special focus on the contribution of $e-\rm H_2$ interaction. Within a cluster virial expansion, the Beth-Uhlenbeck formula is applied to infer the contribution of bound and scattering states to the temperature dependent second virial coefficient. The scattering states are calculated using the phase expansion method with the polarization interaction model that incorporates experimental data for the $e-\rm H_2$ scattering cross section. We present results for the scattering phase shifts, differential scattering cross sections, the second virial coefficient due to $e-\rm H_2$ interaction. The influence of this interaction on the composition of the partially ionized hydrogen plasma is confined to the parameter range where both the $\rm H_2$ and the free electron components are abundant.