MOLECULAR ROTATION IN SUPERFLUID $^{4}He$ NANODROPLETS: THE VALIDITY OF A HYDRODYNAMIC MODEL

$^{a}$C. Callegari, A. Conjusteau, I. Reinhard, K.K. Lehman, G. Scoles, and F. Dalfovo, Phys. Rev. Lett. 83, 5058 (1999); ibid. 84, 1848(E) (2000). $^{b}$E. Draeger and D.M. Ceperley, private communication.Author Institution: Department of Chemistry, Princeton University; Dipartimento di Matematica e Fisica, Universit\`{a} Cattolica del Sacro CuoreIn order to accurately predict the effective moments of inertia $(I_{eff})$ of linear molecules rotating in superfluid $^{4}He$ droplets, we have recently devised a superfluid hydrodynamic model. In the present implementation, the helium density profile induced by the He-molecule interaction potential is first calculated at the Density Functional level, and then used as the input of the hydrodynamic equation for the irrotational motion of a viscousless fluid. The kinetic energy of the fluid $(E_{k})$ is then used to calculate $I_{eff}$ via: $E_{k} = \frac{1}{2} \Delta I\omega^{2}$, where $\omega$ is the angular velociiy of the molecule, and $\Delta $I is the difference between $I_{eff}$, and the moment of inertia of the bare $molecule.^{a}$ The model relies on the assumption that the density of the fluid in the rotating frame of reference is independent of $\omega$ and can therefore be calculated in the limit of a static molecule (adiabatic following approximation). The validity of this approximation, and its first-order corrections will be discussed. The advantages and limitations of Density Functional Theory for calculating me true helium density will also be addressed, in a comparison with Quantum Monte Carlo results which recently became available for HCN and its $oligomers.^{b}