Quantum Neutron Scattering — Feynman Paths Information, Weak Values and Intensity Deficit Effect

Abstract The conventional theory of non-relativistic neutron beam scattering from many-body systems treats the beam essentially as a classical system, because the neutron dynamical variables are captured in the main theoretical formulas (e.g. time-correlation functions) not as quantum mechanical operators but as c-numbers only. This simplification results in the full decoupling of the probe particles’ dynamics from the quantum dynamics of the scatterer. Further, neutrons’ wavefunctions are represented with plane waves, and thus the concept of neutron’s finite coherence length in momentum space becomes irrelevant. Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, Feynman paths, “which-path information” versus interference, Weak Values theory) new observable effects of non-relativistic quantum beam scattering may be exposed and/or predicted, such as a surprising intensity deficit in neutron Compton scattering (NCS) of epithermal neutrons from protons of H-containing materials. Here, the NCS-intensity deficit observed in scattering from liquid C 6 H 6 is discussed and interpreted from first principles, in the general frame of Weak Values theory. Moreover, based on Feynman’s didactical argument that there isn’t any interference between distinguishable neutron paths, we show that this NCS-effect cannot be interpreted as being caused by destructive interference of neutron paths scattered from entangled (two or a few) protons, as was earlier proposed by some authors.