We have compared the TeV \gamma -rays with the new ^ { 12 } CO J =2–1 data toward HESS J1745-303 in the Galactic center and confirmed that molecular cloud MG358.9-0.5 toward ( l,b ) = ( \timeform { 358.9 D } , \timeform { -0.5 D } ) at V _ { \mathrm { LSR } } = -100 – 0 km s ^ { -1 } shows a reasonable positional agreement with the primary peak ( northern part ) of the \gamma -ray source .
For the southern part of HESS J1745-303 , we see no CO counterpart , whereas the H \emissiontype I gas in the SGPS H \emissiontype I dataset shows a possible counterpart to the \gamma -ray source .
This H \emissiontype I gas may be optically thick as supported by the H \emissiontype I line shape similar to the optically thick ^ { 12 } CO. We estimate the total mass of interstellar protons including both the molecular and atomic gas to be 2 \times 10 ^ { 6 } \MO and the cosmic-ray proton energy to be 6 \times 10 ^ { 48 } ergs in the hadronic scenario .
We discuss possible origins of the cosmic-ray protons including the nearby SNR G359.1-0.5 .
The SNR may be able to explain the northern \gamma -ray source but the southern source seems to be too far to be energized by the SNR .
As an alternative , we argue that the second-order Fermi acceleration in the inter-clump space surrounded by randomly moving high-velocity clumps may offer a possible mechanism to accelerate protons .
The large turbulent motion with velocity dispersion of \sim 15 km s ^ { -1 } has energy density two orders of magnitude higher than in the solar vicinity and is viable as the energy source .