  We study the effect of magnetic field and geometric confinement on excitons
confined to a quantum ring. We use analytical matrix elements of the Coulomb
interaction and diagonalize numerically the effective-mass Hamiltonian of the
problem. To explore the role of different boundary conditions, we investigate
the quantum ring structure with a parabolic confinement potential, which allows
the wavefunctions to be expressed in terms of center of mass and relative
degrees of freedom of the exciton. On the other hand, wavefunctions expressed
in terms of Bessel functions for electron and hole are used for a hard-wall
confinement potential. The binding energy and electron-hole separation of the
exciton are calculated as function of the width of the ring and the strength of
a external magnetic field. The linear optical susceptibility as a function of
magnetic fields is also discussed. We explore the Coulomb electron-hole
correlation and magnetic confinement for several ring width and size
combinations. The Aharanov-Bohm oscillations of exciton characteristics
predicted for one-dimensional rings are found to not be present in these
finite-width systems.

Mesoscale and Nanoscale Physics;Materials Science