  Models play an important role in our understanding of the global structure of
the solar wind and its interaction with the interstellar medium. A critical
ingredient in many types of models are the charge-exchange collisions between
ions and neutrals. Some ambiguity exists in the charge-exchange cross-section
for protons and hydrogen atoms, depending on which experimental data is used.
The differences are greatest at low energies, and for the plasma-neutral
interaction in the outer heliosheath may exceed 50\%. In this paper we assess a
number of existing data sets and formulae for proton-hydrogen charge-exchange.
We use a global simulation of the heliosphere to quantify the differences
between the currently favored cross-section, and a formulation we suggest that
more closely matches the majority of available data. We find that in order to
make the resulting two heliospheres the same size, the interstellar proton and
hydrogen densities need to be adjusted by 10 to 15\%, which provides a way to
link the uncertainty in the cross-section to the uncertainty in the parameters
of the pristine interstellar plasma.
