Suzaku observations of a TeV unidentified (unID) source, HESS J1745-303, are presented. A possible excess of neutral iron line emission is discovered, and is likely associated with the main part of HESS J1745-303, named region A. It may be an X-ray reflection nebula where the X-rays from previous Galactic Center (GC) activity are reflected by a molecular cloud. This result further strengthens the assumption that the molecular cloud which is spatially coincident with region A of HESS J1745-303 is located in the GC region. The TeV emission from molecular clouds is reminiscent of the diffuse TeV gamma-rays from the GC giant molecular clouds, and it could have the same emission mechanism. With deep exposure mapping observations by Suzaku, a tight upper-limit on the 2-10 keV continuum diffuse emission from region A is obtained, as 2.1x10^-13ergs s^-1cm^-2. The flux ratio between 1-10 TeV and 2-10 keV is larger than 4. Possible scenarios to reproduce wide-band spectra from keV to TeV are examined. Thermal X-rays from nearby two old supernova remnants, G359.0-0.9 and G359.1-0.5, are detected, and their emission properties are well determined in the present study with deep exposure.
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