Kelvin circulation in a cranked anisotropic oscillator + BCS mean field

The Kelvin circulation vector is the hermitian kinematical observable that measures the true character of nuclear rotation. For a rotating deformed nucleus modeled by a self-consistent cranked anisotropic oscillator mean field with BCS pairing, the expectation value of the Kelvin circulation operator depends upon the deformation and upon the strength of the pairing field. For zero pairing, the circulation acquires its rigid rotor value. As the pairing field increases, the circulation tends to zero, the irrotational flow limit. At critical values of the pairing field, the deformation and circulation make abrupt phase transitions