A renormalized equation for the three-body system with short-range interactions
Abstract
We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.
Cite
@article{arxiv.nucl-th/0011024,
title = {A renormalized equation for the three-body system with short-range interactions},
author = {H. -W. Hammer and Thomas Mehen},
journal= {arXiv preprint arXiv:nucl-th/0011024},
year = {2009}
}
Comments
12 pages, RevTex, 2 ps figures, included with epsf.tex