  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).
