Gas-phase recombination, grain neutralization and cosmic-ray ionization in diffuse gas

Atomic ions are mostly neutralized by small grains (or PAH molecules) in current theories of heating and cooling in cool diffuse clouds; in the main they do not recombine with free electrons. This alters the ionization balance by depressing n(H+) and n(He+) while carbon generally remains nearly fully once-ionized: charge exchange with atomic oxygen and formation of H2 and OH also depress n(H+) in partly molecular gas. Seemingly restrictive empirical limits on the cosmic ray ionization rate of hydrogen ($\zeta_H$) are relaxed and faster rates are favored in a wide range of circumstances, when grain neutralization is recognized. Maintenance of the proton density at levels needed to reproduce observations of HD requires $\zeta_H$ at least 2x10^{-16} s^{-1}, but such models naturally explain the presence of both HD and H3^+ in relatively tenuous H I clouds. In dense gas, a higher ionization rate can account for high observed fractions of atomic hydrogen, and recognition of the effects of grain neutralization can resolve a major paradox in the formation of sulfur-bearing compounds.