Differential scattering of spin±1/2 polarized neutrons by chiral systems. III. Coupled oscillator model

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Abstract
The general theory of polarized neutron scattering by nonmagnetic chiral systems (see Ref. 1) is applied to a specific model system comprised of vibrating nuclei. The model scattering system is made up of two ’’spinless’’ nuclei constrained by external (crystal or molecular) force fields to vibrate as linear (harmonic) oscillators along mutually orthogonal, laboratory-fixed directions. Interactions between the two vibrating nuclei are introduced so that the dynamics of the two linear oscillators are coupled. This coupled oscillator system is constructed to reflect the chirality of the local force fields in the scattering medium. The vibrational states of the chiral coupled oscillator system lack parity, and it is shown that left-handed and right-handed polarized neutrons are scattered differentially by vibrational excitations (and de-excitations) within the system. Calculations are performed to estimate the magnitude of this differential polarized neutron scattering, and the detectability of this phenomenon is assessed.

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