  The recent development of techniques for laser-driven shock compression of
hydrogen has opened the door to the experimental determination of its behavior
under conditions characteristic of stellar and planetary interiors. The new
data probe the equation of state (EOS) of dense hydrogen in the complex regime
of pressure ionization. The structure and evolution of dense astrophysical
bodies depend on whether the pressure ionization of hydrogen occurs
continuously or through a ``plasma phase transition'' (PPT) between a molecular
state and a plasma state. For the first time, the new experiments constrain
predictions for the PPT. We show here that the EOS model developed by Saumon
and Chabrier can successfully account for the data, and we propose an
experiment that should provide a definitive test of the predicted PPT of
hydrogen. The usefulness of the chemical picture for computing astrophysical
EOS and in modeling pressure ionization is discussed.
