Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach

Abstract

Detailed in this manuscript is a methodology to model ground state properties of ⁴He droplets at zero pressure and zero Kelvin using a density functional theory of liquid helium. The density functional approach examined here consists of two noted functionals from the literature and corresponding mean field definitions. A mean field and trial density are defined for each system and optimized to self-consistency using a matrix diagonalization technique. Initial calculations of planar slabs are performed and demonstrate reasonable agreement with experiment and with prior studies using density functional theory. Quantum properties of droplets and droplets containing atomic dopants are calculated. Three different He-dopant potentials are examined to test the limits of the functional methods. For each impurity interaction, an average of 12 atoms were found to reside in the first solvation shell with an atomic dopant placed at the droplet center. Maximum densities in the first solvation shell reached those of solid helium as predicted by DF methods.