Helium dimers and trimers within carbon nanotubes

Abstract

Helium dimers and trimers in infinite carbon nanotubes are described by wave function constructed as a product of Jastrow–Feenberg (JF) pair correlation and one-particle functions. One-particle functions are the ground state eigenfunctions of one helium atom in the tube; their analytic form is derived by fitting the corresponding numerical solution. Using this function in the Monte Carlo (MC) calculations in two successive stages, VMC (simple variational MC) and DMC (diffusion MC), it is found that binding strongly depends on the tube radius. Among armchair nanotubes binding is the strongest for the (7,7) nanotube. In that case the average distance between helium atoms in dimers and trimers is between 5 and 10 A ̊ . For larger radii the energies of 3 He dimers and trimers are the same within the errorbars, indicating the possible dimerized structure. In the (5,5) nanotube, the binding energies of boson 4 He 3 and fictitious fermion trimer, which has the same mass as 4 He 3 and spin 1 2 , are within the errorbars.