An analysis of neutral interstellar gas in the γ-ray middle-aged supernova remnants (SNRs) is presented. We carried out multi-line CO observations of 12CO(J = 1–0) and 12CO(J = 2–1) toward three middle-aged SNRs, W44, IC 443 and W28, with the NANTEN2 telescope. For all three SNRs, we identified the shocked molecular gas which has high-velocity wing emission and the high 12CO J = 2–1/1–0 line intensity ratio of greater than 1. The distribution of these shocked gas has the good correlation with that of GeV–TeV γ-rays, which indicates these γ-rays originate from hadronic process and the interaction between SNR shock and clouds plays an major role in the cosmic-ray acceleration for these SNRs. By combining CO results with archive H I data, we derived the amount of total interstellar protons responsible for the γ-rays. Every SNRs have the averaged proton densities ranged from a few hundred to less than 103 cm−3 and we estimated the total cosmic-ray proton energy to be ∼ 1048–1049 erg as lower limits.

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