Theoretical studies of atomic scale impurities in superfluid ⁴He

Abstract

The macroscopic properties of superfluid helium are well known and their microscopic background is understood to a good extent. However, the microscopic description of superfluid in the presence of atomic scale anisotropy, for example, an atom or a molecule, is not complete and it has been extensively studied in the recent years. Especially, the dynamic properties have remained as a challenge. The earlier theoretical studies on atomic scale impurities in superfluid ⁴He have mainly used the standard (classical) bubble model, the quantum Monte Carlo methods, or the one-dimensional density functional theory, all of which having their own specific restrictions. In the present thesis, a fully three-dimensional bosonic density functional method is developed, which enables the study of a variety of time-dependent and time-independent, anisotropic systems. Fully three-dimensional systems are computationally very demanding and an efficient numerical implementation is crucial. Thus a lot of attention must be paid to the design of the implementation. The developed method was applied to three different systems: 1) molecular hydrogen solvated in bulk superfluid helium, 2) a hypothetical two-level atom in a helium droplet, and 3) electron bubbles in bulk superfluid. The solvation of the first four triplet states of H₂ was studied using the bosonic density functional method and a hybrid density functional - diffusion Monte Carlo method. The solvation structures as well as absorption and emission spectra were calculated. The absorption spectrum of a hypothetical two-level atom, which is excited from its anisotropic (isotropic) ground state to its isotropic (anisotropic) excited state, was simulated by recording the time evolution of the system. The absorption spectra obtained are compared with the corresponding isotropic cases and the spectra were found essentially equal in small helium droplets. Electron bubbles in superfluid ⁴He were calculated using a combination of electronic and bosonic density functional methods. As a result, the properties of the first three states of one-electron bubbles were obtained and the two-electron bubble was found unstable in its both (singlet and triplet) states.