Differential scattering of spin ± (1/2) polarized neutrons by chiral systems. I. Theory

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Abstract
A theoretical model is developed for treating the scattering of longitudinally polarized neutrons by a chiral array of nuclei. The model is restricted to consideration of nonmagnetic scattering systems comprised of ’’spinless’’ nuclei, and only forward scattering is considered. The differential scattering of spin ± (1/2) polarized neutrons is presumed to arise via a ’’spin–orbit’’ coupling mechanism in which the spin of the neutron is coupled to the orbital (vibrational) motions of the nuclei in the neutron–nuclei interaction region. Only low‐energy neutron scattering by vibrational excitations (or deexcitations) is considered. Neutron–nuclei interactions are described in terms of (1) neutron absorption–emission processes; (2) neutron reflection processes; and (3) neutrons moving through the (long‐range) Coulombic field of the nuclei. General expressions are developed for the differential scattering amplitudes of spin ± (1/2) polarized neutrons interacting with nuclei undergoing chiral vibrational motion.