Investigating the Properties of Superfluid He-4 through Density Functional Calculations

We present a study of isotopically pure He-4 systems evaluated using helium density functional theory (He-DFT) with the intent of better understanding their ground state structural and energetic properties, particularly within the scope of singularly-doped helium droplets. We self-consistently solve for the density profiles and chemical potentials for a wide range of pure helium droplet sizes (up to 9500 atoms) via an imaginary time propagation method, and fit the resultant energetic data to a power law formula to be able to extrapolate values for even larger droplets. Subsequent calculations on singularly-doped droplets within the same size range yield accurate binding energies for atomic dopants. We then suggest a method of predicting droplet size distributions after pickup of a dopant atom based on an initial distribution and a particular quantity of imparted energy using chemical potential values predicted from our He-DFT calculations, with the intent of providing a means for understanding data generated by helium droplet calorimetry experiments. Along the way, we also rigorously analyze four of the most popular helium density functionals published in the literature in terms of their robustness, computational cost, and accuracy. To conclude, we perform He-DFT simulations of systems that deviate far from bulk helium behavior in order to evaluate the capabilities of the He-DFT method in such scenarios. We find that a density functional treatment of both small and strongly bound droplets is a surprisingly adequate and efficient alternative to more powerful quantum Monte Carlo calculations.