Hammer, H-W; Mehen, T, *A renormalized equation for the three-body system with short-range interactions*,
Nuclear Physics A, vol. 690 no. 4
(2001),
pp. 535-546 [doi] .
**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. © 2001 Elsevier Science B.V.*