摘要： Recently, the notions of Weak Measurement (WM), Weak Value (WV) and Two-State-Vector Formalism (TSVF), firstly introduced by Aharonov and collaborators, have extended the theoretical frame of standard quantum mechanics, thus providing a quantum-theoretical formalism for extracting new information from a system in the limit of small disturbance to its state. Here we provide an application to the case of two-body scattering with one body weakly interacting with its environment — e.g. a neutron being scattered from a H2 molecule physisorbed in a carbon nanotube. In particular, we make contact with the field of incoherent inelastic neutron scattering from condensed systems. We provide a physically compelling prediction of a new quantum effect — a momentum transfer deficit; or equivalently, an enhanced energy transfer; or an apparent reduction of the mass of the struck particle. E.g., when a neutron collides with a H2 molecule in a C-nanotube and excites its translational motion along the nanotube, it apparently exchanges energy and momentum with a fictitious particle with mass of 0.64 atomic mass units. Experimental results are shown and discussed in the new theoretical frame. The effect under consideration has no conventional interpretation, thus also supporting the novelty of the quantum theoretical framework of WV and TVSF. Some speculative remarks about possible applications being of technological interest (fuel cells and hydrogen storage; Li+ batteries; information and communication technology) are shortly mentioned.