Square-well solution to the three-body problem

Abstract

The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles and two identical spin-1/2 fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to arbitrary potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where for example large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving is substantial.

34 pages, LaTeX file, 9 postscript figures included using epsf.sty

Cited by in corpus (24)

• Benchmark Test Calculation of a Four-Nucleon Bound State
• The structure of the atomic helium trimers: Halos and Efimov states
• Comparing and contrasting nuclei and cold atomic gases
• Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter
• Three-body halos. V. Computations of continuum spectra for Borromean nuclei
• Range Corrections to Three-Body Observables near a Feshbach Resonance
• Efimov Physics and the Three-Body Parameter within a Two-Channel Framework
• The ${}^{10}$Li spectrum and the ${}^{11}$Li properties
• Regularization of a three-body problem with zero-range potentials
• Borromean ground state of fermions in two dimensions
• Phase equivalent potentials for three-body halos
• Correlated Trapped Bosons and the Many-Body Efimov Effect
• Two-body correlations in N-body boson systems
• Regularized zero-range model and an application to the triton and the hypertriton
• Correlated N-boson systems for arbitrary scattering length
• Two-body correlations in Bose condensates
• Classification of three-body quantum halos
• Structure of boson systems beyond the mean-field
• Efimov states in asymmetric systems
• Occurrence conditions for two-dimensional Borromean systems
• Realistic Ghost State : Pauli Forbidden State from Rigorous Solution of the Alpha Particle
• Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions
• Comment on "New modes of halo excitations in the 6He nucleus"
• Origin of Borromean systems