The supernova remnant (SNR) G338.3-0.0 spatially correlates with HESS J1640-465, which is considered the most luminous gamma-ray source associated with a SNR in our Galaxy. The X-ray pulsar PSR J1640-4631 has been recently discovered within the SNR shell, which could favor a leptonic origin for the detected very-high energy (VHE) emission. In spite of this, the origin of the VHE radiation from HESS J1640-465 has not been unambiguously clarified so far. Indeed, a hadronic explanation cannot be ruled out by current observations. On the basis of atomic (HI) and molecular (12^CO) archival data, we determine, for the first time, the total ambient density of protons in the region of the G338.3-0.0/HESS J1640-465 system, a critical parameter for understanding the emission mechanisms at very high energies. The value obtained is in the 100-130 cm^-3 range. Besides this, we developed a new hadronic model to describe the spectral energy distribution (SED) of the HESS J1640-465 source, which includes the latest total gamma-ray cross-section for proton-proton collisions available in the literature. By using the assessed ambient proton density, we found that the total energy in accelerated protons required to fit the data is 5.4^{+4.7}_{-2.3} x 10^49 erg and 1.6^{+1.4}_{-0.7} x 10^50 erg for a source distance of 8.5 and 13 kpc, respectively. The case where the source distance is 8.5 kpc agrees with the typical scenario in which the energy released is on the order of 10^51 erg and ~10% of that energy is transferred to the accelerated protons, whereas the case corresponding to a source distance of 13 kpc requires either a higher value of the energy released in the explosion or a larger energy fraction to accelerate protons.
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