The results of follow-up observations of the TeV gamma-ray source HESSJ 1640-465 from 2004 to 2011 with the High Energy Stereoscopic System (H.E.S.S.) are reported in this work. The spectrum is well described by an exponential cut-off power law with photon index Gamma=2.11 +/- 0.09_stat +/- 0.10_sys, and a cut-off energy of E_c = (6.0 +2.0 -1.2) TeV. The TeV emission is significantly extended and overlaps with the north-western part of the shell of the SNR G338.3-0.0. The new H.E.S.S. results, a re-analysis of archival XMM-Newton data, and multi-wavelength observations suggest that a significant part of the gamma-ray emission from HESS J1640-465 originates in the SNR shell. In a hadronic scenario, as suggested by the smooth connection of the GeV and TeV spectra, the product of total proton energy and mean target density could be as high as W_p n_H ~ 4 x 10^52 (d/10kpc)^2 erg cm^-3.
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