A Detailed Study of the Molecular and Atomic Gas Toward the {\gamma}-ray
  SNR RX J1713.7-3946: Spatial TeV {\gamma}-ray and ISM Gas Correspondence
  RX J1713.7$-$3946 is the most remarkable TeV $\gamma$-ray SNR which emits
$\gamma$-rays in the highest energy range. We made a new combined analysis of
CO and \ion{H}{1} in the SNR and derived the total protons in the interstellar
medium (ISM). We have found that the inclusion of the \ion{H}{1} gas provides a
significantly better spatial match between the TeV $\gamma$-rays and ISM
protons than the H$_2$ gas alone. In particular, the southeastern rim of the
$\gamma$-ray shell has a counterpart only in the \ion{H}{1}. The finding shows
that the ISM proton distribution is consistent with the hadronic scenario that
comic ray (CR) protons react with ISM protons to produce the $\gamma$-rays.
This provides another step forward for the hadronic origin of the $\gamma$-rays
by offering one of the necessary conditions missing in the previous hadronic
interpretations. We argue that the highly inhomogeneous distribution of the ISM
protons is crucial in the origin of the $\gamma$-rays. Most of the neutral gas
was likely swept up by the stellar wind of an OB star prior to the SNe to form
a low-density cavity and a swept-up dense wall. The cavity explains the
low-density site where the diffusive shock acceleration of charged particles
takes place with suppressed thermal X-rays, whereas the CR protons can reach
the target protons in the wall to produce the $\gamma$-rays. The present
finding allows us to estimate the total CR proton energy to be $\sim 10^{48}$
ergs, 0.1% of the total energy of a SNe.
