We present a new analysis of the interstellar protons toward the TeV $gamma$-ray SNR RX J0852.0$-$4622 (G266.2$-$1.2, Vela Jr.). We used the NANTEN2 $^{12}$CO($J$ = 1-0) and ATCA & Parkes HI datasets in order to derive the molecular and atomic gas associated with the TeV $gamma$-ray shell of the SNR. We find that atomic gas over a velocity range from $V_mathrm{LSR}$ = $-4$ km s$^{-1}$ to 50 km s$^{-1}$ or 60 km s$^{-1}$ is associated with the entire SNR, while molecular gas is associated with a limited portion of the SNR. The large velocity dispersion of the HI is ascribed to the expanding motion of a few HI shells overlapping toward the SNR but is not due to the Galactic rotation. The total masses of the associated HI and molecular gases are estimated to be $sim2.5 times 10^4 $ $M_{odot}$ and $sim10^3$ $M_{odot}$, respectively. A comparison with the H.E.S.S. TeV $gamma$-rays indicates that the interstellar protons have an average density around 100 cm$^{-3}$ and shows a good spatial correspondence with the TeV $gamma$-rays. The total cosmic ray proton energy is estimated to be $sim10^{48}$ erg for the hadronic $gamma$-ray production, which may still be an underestimate by a factor of a few due to a small filling factor of the SNR volume by the interstellar protons. This result presents a third case, after RX J1713.7$-$3946 and HESS J1731$-$347, of the good spatial correspondence between the TeV $gamma$-rays and the interstellar protons, lending further support for a hadronic component in the $gamma$-rays from young TeV $gamma$-ray SNRs.
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