Quantum Beam Scattering—Beam’s Coherence Length, Which-Path Information andWeak Values

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e., with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e., the concept of a neutron’s (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle’s dynamics from the quantum dynamics of the scatterer—a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum-theoretical approaches (e.g., quantum entanglement, “which-path information” versus interference, von Neumann measurement, Weak Values (WV), etc.), new observable effects of non-relativistic quantum beam scattering may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. A new WV-theoretical treatment is provided, which explains both these “deficit effects” from first principles and on equal footing.