  It is shown that, in a conductor carrying a moderate spin current, singlet
pairing can still take place almost as effectively as without a spin current.
The system will still be fully gapped for all spin-up and -down single-particle
excitations, with no depaired electrons. All thermodynamic properties will be
practically the same as without the spin current. All universality relations
and laws of corresponding states found in the theory of Bardeen, Cooper, and
Schrieffer should remain valid. Thus a singlet-pairing superconductor can
always carry a persistent and dissipation-less spin-current. A heuristic
argument to support this conclusion is also given, as well as two possible
experimental tests of this prediction.
