  We have compared the TeV gamma-rays with the new 12CO J=2-1 data toward HESS
J1745-303 in the Galactic center and confirmed that the molecular gas
MG358.9-0.5 toward (l, b)=(358.9, -0.5 at VLSR=-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 HI gas in the Parkes 21 cm HI dataset shows a possible counterpart
to the gamma-ray source. This HI gas may be optically thick as supported by the
HI line shape similar to the optically thick 12CO. We estimate the total mass
of interstellar protons including both the molecular and atomic gas to be
2x10^6 Mo and the cosmic-ray proton energy to be 6x10^{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 ~15 km s-1 has energy density two orders of magnitude
higher than in the solar vicinity and is viable as the energy source.
