Bound states of interacting helium atoms

It is known that most of the paradoxes of modern microscopic theory of superfluidity [1] have to do with the commonly accepted assumption of the single-particle Bose condensate (SBC) prevailing in the quantum structure of the superfluid component. In the He Bose liquid, because of strong interaction, the SBC is strongly suppressed (it comprises no more than 10% of all He atoms [2]), consequently it cannot be the basis of the superfluid component. If in some domain of momentum space there is strong enough attraction between atoms, bound pairs of bosons can form, whence a pair coherent condensate appears, and it is this condensate that will be the basis of the superfluid component. The hypothesis of coupling of helium atoms below the λ point may resolve some of those paradoxes [1,3]. The main purpose of this paper is to explore the possibility of existence of bound states for two interacting He atoms for different theoretical and phenomenological interatomic potentials. We will show that for some of the potentials, discrete levels do exist. Besides, we will analyze certain “quasi-crystallic” models, motivated by the conjecture that at temperatures below the λ point, helium possesses a structure close to that of quantum crystals. Specifically, we will consider a model of atoms “smeared” over a sphere and a Kronig–Penney-type model. These models also allow for pairing of helium atoms; moreover, the Kronig–Penney-type model leads to a band of allowed energies.