Helium trimers and tetramers in two dimensions and quasi-two-dimensions

The ground-state properties of He-3 and He-4 trimers and tetramers in infinite and restricted two-dimensional and quasi-two-dimensional (2D) space are studied. Using Monte Carlo calculation in two stages successively, simple variational Monte Carlo and diffusion Monte Carlo, we find that all trimers (except one of He-3 with spin 3/2) and tetramers are bound. In infinite 2D space the binding energy of He-4 trimer is -183(1) mK and of tetramer -435(1) mK. In the same environment for He-3, using Jastrow-Feenberg-Bruch wave functions trimer (spin 1/2) is bound with -0.013(1) mK and tetramer with -0.021(1) mK. Employing in the same procedure "dimerlike" wave functions for He-3 molecules in infinite 2D space it is discovered that trimer prefers the structure of one dimer and one separate particle while a composition of two separate dimers is preferable for tetramer. In this case binding energies are -0.020(1) mK for trimer and -0.040(1) mK for tetramer. The binding energies of mixed molecules in infinite 2D space are -74.3(4) mK (He-3-He-4(2)); -14(1) mK (He-3(2)-He-4); -254(4) mK (He-3-He-4(3)); -118(2) mK (He-3(2)-He-4(2)); -11(1) mK (He-3(3)-He-4). In holding potentials with well-adjusted parameters there is a drastic increase of binding for trimer and tetramer in both sorts of helium atoms.