We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/Ga0
.7Al0.3As ring at low-magnetic fields. The oscillatory magnetoconductance o
f these systems is systematically studied as a function of density. We obse
rve phase shifts of pi in the magnetoconductance oscillations, and halving
of the fundamental h/e period, as the density is varied. Theoretically we f
ind agreement with the experiment, by introducing an asymmetry between the
two arms of the ring.