  Motivated by recent experiments [A. Lorke {\em et al.}, Phys. Rev. Lett.\
{\bf 84}, 2223 (2000)] an analysis of the ground state and far-infrared
absorption of two electrons confined in a quantum ring is presented. The height
of the repulsive central barrier in the confining potential is shown to
influence in an important way the ring properties. The experiments are best
explained assuming the presence of both high- and low-barrier quantum rings in
the sample. The formation of a two-electron Wigner molecule in certain cases is
discussed.
