Abstract
The differential cross section for the inelastic magnetic scattering of neutrons by superconducting rings is derived theoretically taking account of the interaction of the neutron magnetic moment with magnetic field created by the superconducting current. In this scattering process the neutron kinetic energy increases discretely and, respectively, the number of the magnetic flux quanta trapped in the ring, reduces. Quantitative calculations of the scattering cross section for cold neutrons is carried out for thin film rings from type-II superconductors with the film thickness $d<\lambda$($\lambda$ is the penetration depth).
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