Path-integral simulations of hydrogen and hydrogen plasmas

Feynman path-integral simulations of a system consisting of protons and distinguishable electrons under periodic boundary conditions are presented with the aim of calculating the phase diagram of hydrogen at various temperatures and densities. For a two-electron–two-proton system, for which Fermi statistics can be ignored, the equations of state and the radial distribution functions are obtained, including the effects of temperature and pressure ionization, for temperatures down to 0.68 eV and densities up to 1 g ${\mathrm{cm}}^{\mathrm{-}3}$. These results are compared to other models. Systems with more than two distinguishable electrons are found to be thermodynamically unstable, by collapsing into a cluster at low temperature, suggesting that further simulations be used to investigate the stability of Boltzmann matter.