We present a detailed analysis of the interstellar medium towards the TeV $gamma$-ray sources HESS J1640$-$465 and HESS J1641$-$463 using results from the Mopra Southern Galactic Plane CO Survey and from a Mopra 7 mm-wavelength study. The $gamma$-ray sources are positionally coincident with two supernova remnants G338.3$-$0.0 and G338.5+0.1 respectively. A bright complex of HII regions connect the two SNRs and TeV objects. Observations in the CO(1-0) transition lines reveal substantial amounts of diffuse gas positionally coincident with the $gamma$-ray sources at multiple velocities along the line of sight, while 7 mm observations in CS, SiO, HC$_{3}$N and CH$_{3}$OH transition lines reveal regions of dense, shocked gas. Archival HI data from the Southern Galactic Plane Survey was used to account for the diffuse atomic gas. Physical parameters of the gas towards the TeV sources were calculated from the data. We find that for a hadronic origin for the $gamma$-ray emission, the cosmic-ray enhancement rates are $sim 10^{3}$ and $10^{2}$ times the local solar value for HESS J1640$-$465 and HESS J1641$-$463 respectively.
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