  We show that in the presence of a three-dimensional (Weyl) spin-orbit
coupling, a transverse spin current is generated in response to either a
constant spin-independent force or a time-dependent Zeeman field in an
arbitrary direction. This effect is the non-Abelian counterpart of the
universal intrinsic spin Hall effect characteristic to the two-dimensional
Rashba spin-orbit coupling. We quantify the strength of such an omnidirectional
spin Hall effect by calculating the corresponding conductivity for fermions and
non-condensed bosons. The absence of any kind of disorder in ultracold-atom
systems makes the observation of this effect viable.
