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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 ofCO and \ion{H}{1} in the SNR and derived the total protons in the interstellarmedium (ISM). We have found that the inclusion of the \ion{H}{1} gas provides asignificantly better spatial match between the TeV $\gamma$-rays and ISMprotons 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 showsthat the ISM proton distribution is consistent with the hadronic scenario thatcomic ray (CR) protons react with ISM protons to produce the $\gamma$-rays.This provides another step forward for the hadronic origin of the $\gamma$-raysby offering one of the necessary conditions missing in the previous hadronicinterpretations. We argue that the highly inhomogeneous distribution of the ISMprotons is crucial in the origin of the $\gamma$-rays. Most of the neutral gaswas likely swept up by the stellar wind of an OB star prior to the SNe to forma low-density cavity and a swept-up dense wall. The cavity explains thelow-density site where the diffusive shock acceleration of charged particlestakes place with suppressed thermal X-rays, whereas the CR protons can reachthe target protons in the wall to produce the $\gamma$-rays. The presentfinding allows us to estimate the total CR proton energy to be $\sim 10^{48}$ergs, 0.1% of the total energy of a SNe.

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