Ground-state properties of two-dimensional quantum fluid helium: Variational hypernetted chain methods

We calculate the ground-state energies and the radial distribution functions of two-dimensional quantum fluid4He, mass 3 boson3He and3He within a hypernetted chain and a Fermi hypernetted chain summation method. To get more accurate results, we include three-body correlation functions in the trial wavefunctions and consider the contributions arising from elementary diagrams via scaling approximations. The two-dimensional4He system has a binding energy of 0.84 K at an equilibrium density 0.042 A−2, which is closer to the result of a Green's function Monte Carlo calculation than previous ones, while mass 3 boson3He has 0.286 K at 0.025 A−2. The3He system is not self-bound and therefore not a liquid state due to its statistics and light mass of the3He atom. We calculate the ground-state energy of two-dimensional liquid4He through a Lennard-Jones potential and that of Aziz to compare the results of both. Aziz's potential gives lower and more accurate energies than the Lennard-Jones potential, as in three dimensions.