Adiabatic hyperspherical study of triatomic helium systems

Abstract

The 4 He 3 system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term, to calculate all low-energy properties of the triatomic 4 He system. The bound state energies of the 4 He trimer are computed as well as the 4 He+ 4 He 2 elastic scattering cross sections, the three-body recombination and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4 He and one 3 He atoms, and compute the spectrum of the isotopic trimer 4 He 2 3 He, the 3 He+ 4 He 2 elastic scattering cross sections, the rates for three-body recombination and the collision induced dissociation rate at finite temperatures.The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems.

Momentum-Space Calculation of 4He Triatomic System with Realistic Potential

“…Main features of those realistic potentials are long attractive van der Waals tail and a very strong repulsion at short distances. Especially the latter causes difficulties in calculations of systems containing three or more 4 He atoms. Indeed, even a special form of the differential three-particle Faddeev equations with hard-core potentials has been developed and applied for the study of the three- [1] and four-atom systems [3].…”

“…The main reason is a special feature of 4 He few-atom clusters, namely, an extremely weak binding of fewbody ground states. This weakness of binding is responsible for the manifestation of phenomena such as the Efimov physics or superfluidity; see Ref.…”

“…Systems of 4 He atoms have attracted significant interest, both experimentally and theoretically. The main reason is a special feature of 4 He few-atom clusters, namely, an extremely weak binding of fewbody ground states.…”

“…The dynamics of cold 4 He atoms is essentially governed by the local two-atom potential; there exist a number of realistic parametrizations [7]. Main features of those realistic potentials are long attractive van der Waals tail and a very strong repulsion at short distances.…”

“…The understanding of these phenomena requires precise theoretical calculations of the properties of cold 4 He few-body systems; up to now such calculations with realistic interaction models predominantly have been performed in various coordinate-space frameworks. Three-atom bound (trimer) and scattering states have been calculated solving Faddeev equations [1; 2; 3] or using adiabatic hyperspherical approach [4], while tetramer properties have been obtained solving the Faddeev-Yakubovsky equations [3], using the variational Gaussian expansion method [5] or the hyperspherical Monte-Carlo approach [6]. The latter was extended to more than four atoms and provided estimates for scattering lengths, whereas Ref.…”