Benchmark helium dimer and trimer calculations with a public few-body code

Abstract

We present detailed calculations of bound and scattering states of dimers and trimers of He to produce highly accurate data and to test a non-relativistic three-body code currently in development for public distribution. For these systems, uncertainties and inaccuracies in the fundamental constants frequently used in published works can substantially exceed numerical errors. Our benchmark calculations include specific estimates of the numerical accuracy of the calculations, and also explore sensitivity to fundamental constants and their uncertainties. The use of an inexact coupling constant in the previous calculations leads to 0.08% error for the ground state energy, 0.3% error for the excited state energy and up to 0.15% error for the atom-dimer scattering length in the system of three ${}^4$He atoms. The corresponding errors for the unsymmetric ${}^4$He${}_2^3$He system are 0.3% for the bound state energy and 0.03% for the atom-dimer scattering length.

20 pages, 4 figures, 8 tables

References in corpus (4)

• Adiabatic hyperspherical study of triatomic helium systems
• Description of ${}^4$He tetramer bound and scattering states
• The Three-Boson System at Next-To-Next-To-Leading Order
• Automatic grid construction for few-body quantum mechanical calculations

Cited by in corpus (13)

• Variational calculation of 4He tetramer ground and excited states using a realistic pair potential
• Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials
• Universality in Efimov associated tetramers in 4He
• Universality in molecular halo clusters
• Elusive structure of helium trimers
• Cold atom-dimer reaction rates with ${}^4$He, ${}^{6,7}$Li and ${}^{23}$Na
• The van der Waals interaction as the starting point for an effective field theory
• Approaching universality in weakly-bound three-body systems
• Scattering of cold ${}^4$He on ${}^4$He${-}^{6,7}$Li and ${}^4$He${-}^{23}$Na molecules
• Weakly bound LiHe${}_2$ molecules in the framework of three-dimensional Faddeev equations
• Four-body system of ${}^4\mathrm{He}$ atoms: Dimer-dimer scattering
• Second excited state of ${}^4\mathrm{He}$ tetramer
• Emergence of N-body tunable interactions in universal few-atom system