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In diffuse interstellar clouds the chemistry that leads to the formation of the oxygen-bearing ions OH + , H 2 O + , and H 3 O + begins with the ionization of atomic hydrogen by cosmic rays, and continues through subsequent hydrogen abstraction reactions involving H 2. Given these reaction pathways, the observed abundances of these molecules are useful in constraining both the total cosmic-ray ionization rate of atomic hydrogen (ζ H) and molecular hydrogen fraction (f H 2). We present observations targeting transitions of OH + , H 2 O + , and H 3 O + made with the Herschel Space Observatory along 20 Galactic sight lines toward bright submillimeter continuum sources. Both OH + and H 2 O + are detected in absorption in multiple velocity components along every sight line, but H 3 O + is only detected along 7 sight lines. From the molecular abundances we compute f H 2 in multiple distinct components along each line of sight, and find a Gaussian distribution with mean and standard deviation 0.042 ± 0.018. This confirms previous findings that OH + and H 2 O + primarily reside in gas with low H 2 fractions. We also infer ζ H throughout our sample, and find a lognormal distribution with mean log(ζ H) = −15.75 (ζ H = 1.78 × 10 −16 s −1) and standard deviation 0.29 for gas within the Galactic disk, but outside of the Galactic center. This is in good agreement with the mean and distribution of cosmic-ray ionization rates previously inferred from H + 3 observations. Ionization rates in the Galactic center tend to be 10-100 times larger than found in the Galactic disk, also in accord with prior studies.

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