A renormalized equation for the three-body system with short-range interactions

Journal Article (Journal Article)

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. © 2001 Elsevier Science B.V.

Full Text

Duke Authors

Cited Authors

  • Hammer, HW; Mehen, T

Published Date

  • July 30, 2001

Published In

Volume / Issue

  • 690 / 4

Start / End Page

  • 535 - 546

International Standard Serial Number (ISSN)

  • 0375-9474

Digital Object Identifier (DOI)

  • 10.1016/S0375-9474(00)00710-7

Citation Source

  • Scopus