  The electronic structure of radially polarized excitons in structured
nanorings is analyzed, with emphasis in the ground-state properties and their
dependence under applied magnetic fields perpendicular to the ring plane. The
electron-hole Coulomb attraction has been treated rigorously, through numerical
diagonalization of the full exciton Hamiltonian in the non-interacting
electron-hole pairs basis. Depending on the relative weight of the kinetic
energy and Coulomb contributions, the ground-state of polarized excitons has
"extended" or "localized" features. In the first case, corresponding to small
rings dominated by the kinetic energy, the ground-state shows Aharonov-Bohm
(AB) oscillations due to the individual orbits of the building particles of the
exciton. In the localized regime, corresponding to large rings dominated by the
Coulomb interaction, the only remaining AB oscillations are due to the magnetic
flux trapped between the electron and hole orbits. This dependence of the
exciton, a neutral excitation, on the flux difference confirms this feature as
a signature of Coulomb dominated polarized excitons. Analytical approximations
are provided in both regimens, which accurate reproduce the numerical results.
