  Using analytical expressions for the magnetization textures of thin
submicron-sized magnetic cylinders in vortex state, we derive closed-form
algebraic expressions for the ensuing small-angle neutron scattering (SANS)
cross sections. Specifically, for the perpendicular and parallel scattering
geometries, we have computed the magnetic SANS cross sections for the case of
small vortex-center displacements without formation of magnetic charges on the
side faces of the cylinder. The results represent a significant qualitative and
quantitative step forward in SANS-data analysis on isolated magnetic
nanoparticle systems, which are commonly assumed to be homogeneously or
stepwise-homogeneously magnetized. We suggest a way to extract the fine details
of the magnetic vortex structure during the magnetization process from the SANS
measurements in order to help resolving the long standing question of the
magnetic vortex displacement mode.
