  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.
