  Motivated by recent experiments, we study normal-phase rotating He-3 droplets
within Density Functional Theory in a semi-classical approach. The sequence of
rotating droplet shapes as a function of angular momentum are found to agree
with those of rotating classical droplets, evolving from axisymmetric oblate to
triaxial prolate to two-lobed shapes as the angular momentum of the droplet
increases. Our results, which are obtained for droplets of nanoscopic size, are
rescaled to the mesoscopic size characterizing ongoing experimental
measurements, allowing for a direct comparison of shapes. The stability curve
in the angular velocity-angular momentum plane shows small deviations from the
classical rotating drop model predictions, whose magnitude increases with
angular momentum. We attribute these deviations to effects not included in the
simplified classical model description of a rotating fluid held together by
surface tension, i.e. to surface diffuseness, curvature and finite
compressibility, and to quantum effects associated with deformation of the He-3
Fermi surface. The influence of all these effects is expected to diminish as
the droplet size increases, making the classical rotating droplet model a quite
accurate representation of He-3 rotation.
