  The magnetic field effects on excitons in an InAs nano-ring are studied
theoretically. By numerically diagonalizing the effective-mass Hamiltonian of
the problem, which can be separated into terms in centre-of-mass and relative
coordinates, we calculate the low-lying exciton energy levels and oscillator
strengths as a function of the width of the ring and the strength of the
external magnetic field. The analytical results are obtained for a narrow-width
nano-ring in which the radial motion is the fastest one and adiabatically
decoupled from the azimuthal motions. It is shown that in the presence of
Coulomb correlation, the so called Aharonov-Bohm effect of excitons exists in a
finite (but small) width nano-ring. However, when the ring width becomes large,
the non-simply-connected geometry of nano-rings is destroyed and in turn yields
the suppression of Aharonov-Bohm effect. The conditional probability
distribution calculated for the low-lying exction states allows identification
of the presence of Aharonov-Bohm effect. The linear optical susceptibility is
also calculated as a function of the magnetic field, to be confronted with the
future measurements of optical emission experiments on InAs nano-rings.
