Variational Monte Carlo calculations of ground states of liquidHe4andHe3drops

Variational Monte Carlo calculations of the ground states of drops containing 8–728 atoms of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and 20–240 atoms of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been made. The variational wave functions include two- and three-body correlations and (for the Fermi drops) Feynman-Cohen backflow. We discuss the wave functions, their relation to modern variational wave functions for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, the calculational techniques, and the results for the ground-state energies and density profiles. Our calculations indicate that ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ drops with more than 40 atoms are bound, while a drop with 20 atoms is in a metastable state that has positive energy but negative chemical potential. The surface tensions of both liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are obtained by liquid-drop fits to the calculated binding energies. From the density profiles of the largest drops we estimate the surface thickness of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ to be 7 Å while that for liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is 8 Å.