Summary. --A general scheme is proposed for the interpretation of the phenomena involving low-energy hydrogen-isotope fusion. This scheme is especially developed for the interpretation of the fusion rate observed after the impact of heavy-water clusters (D20)~, 25 ~< n <~ 1350, onto targets of titanium deuteride TiD. It is shown that 1) the impinging energy of large clusters or molecules is equiparted among a lot of target atoms which are brought in collective motion; 2) data can conveniently be represented in an Arrhenius plot; 3) this plot suggests that fusion is a thermally activated process from a metastable precursor; 4) the activation energy for the precursor formation is E* ---2 E0 (E0 being the electron binding energy in the hydrogen atom), and 5) the activated precursor can reasonably be identified with the metastable binuclear heliumlike (D § D+)2e -atom. PACS 25.45.Z -2H-induced reactions and scattering. PACS 79.20.Nc -Atom, molecule, and ion impact. PACS 52.50.Dg -Plasma sources.