  This paper deals with the study of the phase transition of the wave functions
of a segregated two-component Bose-Einstein condensate under Rabi coupling.
This yields a system of two coupled ODE's where the Rabi coupling is linear in
the other wave function and acts against segregation. We prove estimates on the
asymptotic behaviour of the wave functions, as the strength of the interaction
gets strong or weak. We also derive limiting problems in both cases.
