Bias in the temperature of helium nanodroplets measured by an embedded rotor

The ro--vibrational spectra of molecules dissolved in liquid $^4$He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the ripplons of the droplet. This bias grows with both the total angular momentum of the droplet and with the moment of inertia of the solute molecule.Comment: 6 pages, 1 figure, to be published in Journal of Chemical Physic

Potential of a neutral impurity in a large 4^4He 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.Comment: 25 pages, 1 table, 13 figures, to be published in Molecular Physic

Potential of an ionic impurityin a large 4^4He cluster

This paper presents an analysis of the motion of an impurity ion in a nanometer scale $^4$He cluster. Due to induction forces, ions are strongly localized near the center of the cluster, with a root mean squared thermal displacements of only a few \AA. The trapping potential is found to be nearly harmonic, with a frequency of 2.3(1.0) GHz for a positive (negative) ion in a He cluster of radius 5 nm. The anharmonicity is small and positive (energy increases slightly faster than linear with quantum number). It is suggested that by using frequency sweep microwave radiation, it should be possible to drive the ion center of mass motion up to high quantum numbers, allowing the study of the critical velocity as a function of cluster size.Comment: 14 pages, 0 figures, To be published in Molecular Physic

Quantum Hydrodynamic Model for the enhanced moments of Inertia of molecules in Helium Nanodroplets: Application to SF6_6

The increase in moment of inertia of SF$_6$ in helium nanodroplets is calculated using the quantum hydrodynamic approach. This required an extension of the numerical solution to the hydrodynamic equation to three explicit dimensions. Based upon an expansion of the density in terms of the lowest four Octahedral spherical harmonics, the predicted increase in moment of inertia is $170 {\rm u \AA^2}$, compared to an experimentally determined value of $310(10) {\rm u \AA^2}$, i.e., 55% of the observed value. The difference is likely in at least part due to lack of convergence with respect to the angular expansion, but at present we do not have access to the full densities from which a higher order expansion can be determined. The present results contradict those of Kwon et al., J. Chem. Phys. {\bf 113}, 6469 (2000), who predicted that the hydrodynamic theory predicted less than 10% of the observed increase in moment of inertia.Comment: 10 pages, including 1 figur

Rotation in liquid 4^4He: Lessons from a toy model

This paper presents an analysis of a model problem, consisting of two interacting rigid rings, for the rotation of molecules in liquid $^4$He. Due to Bose symmetry, the excitation of the rotor corresponding to a ring of N helium atoms is restricted to states with integer multiples of N quanta of angular momentum. This minimal model shares many of the same features of the rotational spectra that have been observed for molecules in nanodroplets of $\approx 10^3 - 10^4$ helium atoms. In particular, this model predicts, for the first time, the very large enhancement of the centrifugal distortion constants that have been observed experimentally. It also illustrates the different effects of increasing rotational velocity by increases in angular momentum quantum number or by increasing the rotational constant of the molecular rotor. It is found that fixed node, diffusion Monte Carlo and a hydrodynamic model provide upper and lower bounds on the size of the effective rotational constant of the molecular rotor when coupled to the helium