Adiabatic hyperspherical study of triatomic helium systems

Abstract

The $^{4}\mathrm{He}_{3}$ 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 $^{4}\mathrm{He}$ system. The bound state energies of the $^{4}\mathrm{He}$ trimer are computed as well as the $^{4}\mathrm{He}+^{4}\mathrm{He}_{2}$ 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 $^{4}\mathrm{He}$ and one $^{3}\mathrm{He}$ atoms, and compute the spectrum of the isotopic trimer $^{4}\mathrm{He}_{2}^{3}\mathrm{He}$, the $^{3}\mathrm{He}+^{4}\mathrm{He}_{2}$ 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.