Binding of Two Helium Atoms in Confined Geometries

We carry out a comprehensive study of the binding of two helium atoms in unrestricted and, in particular, in restricted geometries in both two and three dimensions. Besides the well known binding of the ⁴He dimer in unrestricted geometry in two and three dimensions, we also find weakly bound states of the ³He-⁴He molecule and the ³He dimer in 2 dimensions. Furthermore, any combination of two ⁴He or ³He atoms can form a molecule if their motion is sufficiently confined. Our calculations are carried out by numerically solving the Schrödinger equation as well as by constructing a suitable variational wave function.