Helium 4 dimer in nanotubes

The ground state of the helium 4 dimer is considered using the Monte Carlo technique. In a cylinder with a hard core wall, binding depends on its radius. For a small radius binding occurs as in the one-dimensional case. With an increase of the radius, the binding becomes stronger, reaches its maximum value, and then slowly diminishes. In conical geometry, that may be realized as a generalization of a cylindrical one, this dependence of the binding energy on the radius might lead to an effective force which tends to move the molecule toward the region of minimal energy. Thus, in channels, with nonhomogeneous cross-sections, the particles move easier in dimer form. In addition, the square of the momentum and of the particle separation along the cylinder axis and in the plane perpendicular to it are calculated as well.