Weak Measurement and Two-State-Vector Formalism: Deficit of Momentum Transfer in Scattering Processes

The notions of weak measurement, weak value, and two-state-vector formalism provide a new quantum-theoretical frame for extracting additional information from a system in the limit of small disturbances to its state. Here, we provide an application to the case of two-body scattering with one body weakly interacting with an environment. The direct connection to real scattering experiments is pointed out by making contact with the field of impulsive incoherent neutron scattering from molecules and condensed systems. In particular, we predict a new quantum effect in neutron-atom collisions, namely an observable momentum transfer deficit; or equivalently, a reduction of effective mass below that of the free scattering atom. Two corroborative experimental findings are shortly presented. Implications for current and further experiments are mentioned. An interpretation of this effect and the associated experimental results within conventional theory is currently unavailable.