  The spin-interference that is caused by the Rashba spin-orbit interaction in
a gate-controlled Aharonov-Bohm ring is studied by the analysis of the
conductance oscillations as a function of both the gate voltage and magnetic
field. The scattering matrix approach is used to reveal the effect of the
quantum scatterers connected to two one-dimensional leads on the phase of the
transmission and reflection amplitudes. The variations of the transmission and
reflection amplitudes that are caused by the quantum scatterers for the
particles moving inside and outside rings are shown to define a parity of the
and conductance oscillations.
