The Galactic TeV ${\gamma}$ -ray source ${\mathrm{HESS\,J}1804{-}216}$ is currently an unidentified source. In an attempt to unveil its origin, we present here the most detailed study of interstellar gas using data from the Mopra Southern Galactic Plane CO Survey, 7- and 12-mm wavelength Mopra surveys and Southern Galactic Plane Survey of HI. Several components of atomic and molecular gas are found to overlap ${\mathrm{HESS\,J}1804{-}216}$ at various velocities along the line of sight. The CS(1-0) emission clumps confirm the presence of dense gas. Both correlation and anti-correlation between the gas and TeV ${\gamma}$ -ray emission have been identified in various gas tracers, enabling several origin scenarios for the TeV ${\gamma}$ -ray emission from ${\mathrm{HESS\,J}1804{-}216}$ . For a hadronic scenario, ${\mathrm{SNR\,G}8.7{-}0.1}$ and the progenitor supernova remnant (SNR) of ${\mathrm{PSR\,J}1803{-}2137}$ require cosmic ray (CR) enhancement factors of ${\mathord{\sim} 50}$ times the solar neighbour CR flux value to produce the TeV ${\gamma}$ -ray emission. Assuming an isotropic diffusion model, CRs from both these SNRs require a slow diffusion coefficient, as found for other TeV SNRs associated with adjacent ISM gas. The morphology of gas located at 3.8 kpc (the dispersion measure distance to ${\mathrm{PSR\,J}1803{-}2137}$ ) tends to anti-correlate with features of the TeV emission from ${\mathrm{HESS\,J}1804{-}216}$ , making the leptonic scenario possible. Both pure hadronic and pure leptonic scenarios thus remain plausible.

We investigate the interstellar medium towards seven TeV gamma-ray sources thought to be pulsar wind nebulae using Mopra molecular line observations at 7 mm [CS(1–0), SiO(1–0, v = 0)], Nanten CO(1–0) data and the Southern Galactic Plane Survey/GASS Hi survey. We have discovered several dense molecular clouds co-located to these TeV gamma-ray sources, which allows us to search for cosmic rays coming from progenitor SNRs or, potentially, from pulsar wind nebulae. We notably found SiO(1–0, v = 0) emission towards HESS J1809–193, highlighting possible interaction between the adjacent supernova remnant SNR G011.0–0.0 and the molecular cloud at d ∼ 3.7 kpc. Using morphological features, and comparative studies of our column densities with those obtained from X-ray measurements, we claim a distance d ∼ 8.6 − 9.7kpc for SNR G292.2–00.5, d ∼ 3.5 − 5.6 kpc for PSR J1418–6058 and d ∼ 1.5 kpc for the new SNR candidate found towards HESS J1303–631. From our mass and density estimates of selected molecular clouds, we discuss signatures of hadronic/leptonic components from pulsar wind nebulae and their progenitor SNRs. Interestingly, the molecular gas, which overlaps HESS J1026–582 at d ∼ 5 kpc, may support a hadronic origin. We find however that this scenario requires an undetected cosmic-ray accelerator to be located at d < 10 pc from the molecular cloud. For HESS J1809–193, the cosmic rays which have escaped SNR G011.0–0.0 could contribute to the TeV gamma-ray emission. Finally, from the hypothesis that at most 20% the pulsar spin down power could be converted into CRs, we find that among the studied pulsar wind nebulae, only those from PSR J1809–1917 could potentially contribute to the TeV emission.