HESS J1731-347 (G353.6-0.7) is one of the TeV gamma-ray SNRs which shows the shell-like morphology. We have made a new analysis of the interstellar protons toward the SNR by using both the 12CO(J=1-0) and HI datasets. The results indicate that the TeV gamma-ray shell shows significant spatial correlation with the interstellar protons at a velocity range from -90 km/s to -75 km/s, and the distance corresponding to the velocity range is ~5.2 kpc, a factor of 2 larger than the previous figure 3 kpc. The total mass of the interstellar protons is estimated to be 6.4x10^4 M_sun, 25 % of which is atomic gas. We have identified the cold HI gas observed as self-absorption which shows significant correspondence with the northeastern gamma-ray peak. While the good correspondence between the interstellar protons and TeV gamma-rays in the north of the SNR lends support to the hadronic scenario for the TeV gamma-rays, the southern part of the shell shows a break in the correspondence; in particular, the southwestern rim of the SNR shell shows a significant decrease of the interstellar protons by a factor of 2. We argue that this discrepancy can be explained as due to leptonic gamma-rays, because this region well coincides with the bright shell which emit non-thermal radio continuum emission and non-thermal X-rays, suggesting that the gamma-rays of HESS J1713-347 consist of both the hadronic and leptonic components. The leptonic contribution then corresponds to ~20 % of the total gamma-rays. The total energy of cosmic-ray protons is estimated to be 10^49 erg for the gamma-ray energy range of 1 GeV - 100 TeV by assuming that 80 % of the total gamma-ray is of the hadronic origin.
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