Single-particle orbitals in liquid-helium drops

Drops containing 20 to 240 atoms of Bose liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and Fermi liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are studied by variational Monte Carlo methods as simple examples of correlated inhomogeneous quantum systems. In the present work we report wave functions of natural, quasiparticle, and mean-field orbitals in these drops. The wave functions of natural orbitals are determined by diagonalizing the one-particle density matrix. The condensate fraction and wave function in the Bose-liquid drops are calculated. The quasihole states are defined in the spirit of Landau’s theory, and their wave functions are calculated from the overlaps between states containing N and N-1 atoms. In Bose-liquid drops the wave function of the quasihole orbital is similar to that of the condensate; however, in Fermi-liquid drops the quasihole wave functions are different from those of natural or mean-field orbitals. We find that a simple local-density approximation provides an accurate relation between the mean-field and quasihole wave functions for both Bose- and Fermi-liquid drops. The wave functions of natural orbitals are very localized and simple methods to construct them from mean-field wave functions are also discussed. The momentum distributions of atoms in the drops are calculated and compared with those of extended liquids. The deviations of the momentum distributions from mean-field distributions are also discussed.