We report observations and analysis of infrared spectra of H-3(+) and CO lines in the Galactic center, within a few parsecs of the central black hole, Sgr A*. We find a cosmic ray ionization rate typically an order of magnitude higher than outside the Galactic center. Notwithstanding, the elevated cosmic ray ionization rate is 4 orders of magnitude too short to match the proton energy spectrum, as inferred from the recent discovery of the TeV gamma-ray source in the vicinity of Sgr A*.