Potential of a neutral impurity in a large $^4$He clusters

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.