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 H i 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 H i is ascribed to the expanding motion of a few H i shells overlapping toward the SNR but is not due to the Galactic rotation . The total masses of the associated H i and molecular gases are estimated to be \sim 2.5 \times 10 ^ { 4 } M _ { \odot } and \sim 10 ^ { 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 \sim 10 ^ { 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 .