Title

Three bosons in one dimension with short-range interactions: Zero-range potentials

Document Type

Article

Publication Date

9-2005

Abstract

We consider the three-boson problem with δ-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle off a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum-space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the 1+2 scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pairwise interactions are short range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling.

Required Publisher Statement

© 2005 The American Physical Society

Document Object Identifier (DOI)

10.1103/PhysRevA.72.032728

Publication Information

Physical Review A

This document is currently not available here.

Share

COinS