  This paper presents an analysis of the motion of an neutral impurity species
in a nanometer scale $^4$He cluster, extending a previous study of the dynamics
of an ionic impurity. It is shown that for realistic neutral impurity-He
potentials, such as those of SF$_6$ and OCS, the impurity is kept well away of
the the surface of the cluster by long range induction and dispersion
interactions with He, but that a large number of `particle in a box' center of
mass states are thermally populated. It is explicitly demonstrated how to
calculate the spectrum that arises from the coupling of the impurity rotation
and the center of mass motion, and it is found that this is a potentially
significant source of inhomogeneous broadening in vibration-rotation spectra of
anisotropic impurities. Another source of inhomogeneous broadening is the
hydrodynamic coupling of the rotation of the impurity with the center of mass
velocity. A quantum hamiltonian to describe this effect is derived from the
classical hydrodynamic kinetic energy of an ellipsoid. Simple analytic
expressions are derived for the resulting spectral line shape for an impurity
in bulk He, and the relevant matrix elements derived to allow fully quantum
calculations of the coupling of the center of mass motion and rotation for an
impurity confined in a spherical He cluster. Lastly, the hydrodynamic
contribution to the impurity effective moment of inertia is evaluated and found
to produce only a minor fractional increase.
