Context: .The cosmic-ray ionization rate ζCR of dense molecular clouds is a key parameter for their dynamics and chemistry.
Aims: .Variations of ζCR are well established, but it is unclear if these are related to source column density or to Galactic location.
Methods: .Using the APEX telescope, we have mapped the 364 GHz line of H3O+ in the Sgr B2 region and observed the 307 GHz line at selected positions. With the IRAM 30-m telescope we have observed the H218O 203 GHz line at the same positions.
Results: .Strong H3O+ emission is detected over a ~3 × 2 pc region, indicating an H3O+ column density of 1015-1016 cm-2 in an 18” beam. The H3O+ abundance of ~ 3 × 10-9 and H3O+/H2O ratio of ~1/50 in the Sgr B2 envelope are consistent with models with ζCR ~ 4 × 10-16 s-1, 3× lower than derived from H3+ observations toward Sgr A, but 10× that of local dense clouds.
Conclusions: .The ionization rates of interstellar clouds thus seem to be to first order determined by the ambient cosmic-ray flux, while propagation effects cause a factor of ~3 decrease from diffuse to dense clouds.

