Path Integral Studies of the Rotations of Methane and Its Heavier Isotopomers in 4He Nanoclusters

Path integral Monte Carlo simulations have been carried out to study the rotations of a methane molecule and its heavier isotopomers inside a small cluster of He-4 atoms at 0.3 K in order to determine how the renormalization in the methane's rotational constant is related to the quantum statistics and superfluidity of the helium shell. By changing the mass of the hydrogens and systematically varying the moment of inertia of the methane, we were able to study the effects of its rotations on the quantum statistics of the helium atoms and their countereffects on the methane's effective rotational constant. The renormalized rotational constant depends strongly on the intrinsic moment of inertia of the methane. A heavy probe favors strong templating of the helium density as well as a large renormalization in the probe's rotational constant, but a light probe shows almost no effect on the shell density or the effective rotational constant. These results suggest that in order to fully understand the superfluidity of the helium shell, the probe must be treated as an integral part of the system. We rationalize the findings in terms of a rotational smearing effect and suggest that there is no clearly quantifiable relationship between the superfluid fraction of the shell and the renormalized rotational constant of the probe for cases where the probe molecule is either light or has weak anisotropic interactions with the helium atoms.