A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2

Abstract

We present a new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement. The goal is to address Fermi–Dirac and Bose–Einstein nuclear spin statistics on an equal footing and to deliver excited states with a similar accuracy to that of the ground state, implementing ab initio-derived potential models as well. The method is applied to clusters of up to four (three) ⁴He atoms and para-H₂ molecules (³He atoms) inside a single-walled (1 nm diameter) carbon nanotube. Due to spin symmetry effects, the bound states energy landscape as a function of the angular momentum around the tube axis becomes much more complex and rich as the number of ³He atoms increase compared to the spinless ⁴He and para-H₂ counterparts. Four bosonic ⁴He and para-H₂ particles form pyramidal-like structures which are more compact as the particle mass and the strength of the inter-particle interaction increases. They feature stabilization of the collective rotational motion as bosonic quantum rings bearing persistent rotational motion and superfluid flow. Our results are brought together with two key experimental findings from the group of Jan-Peter Toennies: (1) the congestion of spectral profiles in doped ³He droplets as opposed to the case of ⁴He droplets (S. Gebenev, J. P. Toennies and A. F. Vilesov, Science, 1998, 279, 2083); (2) the onset of microscopic superfluidity in small doped clusters of para-H₂ molecules (S. Grebenev, B. G. Sartakov, J. P. Toennies and A. F. Vilesov, Science, 2000, 289, 1532), but at the reduced dimensionality offered by the confinement inside carbon nanotubes.