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The notions of weak measurement, weak value, and two-state-vector formalismprovide a new quantum-theoretical frame for extracting additional informationfrom a system in the limit of small disturbances to its state. Here, we providean application to the case of two-body scattering with one body weaklyinteracting with an environment. The direct connection to real scatteringexperiments is pointed out by making contact with the field of impulsiveincoherent neutron scattering from molecules and condensed systems. Inparticular, we predict a new quantum effect in neutron-atom collisions, namelyan observable momentum transfer deficit; or equivalently, a reduction ofeffective mass below that of the free scattering atom. Two corroborativeexperimental findings are shortly presented. Implications for current andfurther experiments are mentioned. An interpretation of this effect and theassociated experimental results within conventional theory is currentlyunavailable.

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