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

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.