Knowledge Bank

In order to accurately predict the effective moments of inertia $(Ieff)$ of linear molecules rotating in superfluid $\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}He$ 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 $(Ek)$ is then used to calculate $Ieff$ via: $Ek=12\Delta I\omega 2$, where $\omega$ is the angular velociiy of the molecule, and $\Delta $I is the difference between $Ieff$, 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 $oligomers.b$