Chemical Analysis of a Diffuse Cloud along a Line of Sight Toward W51:
  Molecular Fraction and Cosmic-Ray Ionization Rate
  Absorption lines from the molecules OH+, H2O+, and H3+ have been observed in
a diffuse molecular cloud along a line of sight near W51 IRS2. We present the
first chemical analysis that combines the information provided by all three of
these species. Together, OH+ and H2O+ are used to determine the molecular
hydrogen fraction in the outskirts of the observed cloud, as well as the
cosmic-ray ionization rate of atomic hydrogen. H3+ is used to infer the
cosmic-ray ionization rate of H2 in the molecular interior of the cloud, which
we find to be zeta_2=(4.8+-3.4)x10^-16 per second. Combining the results from
all three species we find an efficiency factor---defined as the ratio of the
formation rate of OH+ to the cosmic-ray ionization rate of H---of
epsilon=0.07+-0.04, much lower than predicted by chemical models. This is an
important step in the future use of OH+ and H2O+ on their own as tracers of the
cosmic-ray ionization rate.
