A renormalized equation for the three-body system with short-range interactions
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.
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Related Subject Headings
- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 5106 Nuclear and plasma physics
- 5101 Astronomical sciences
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0201 Astronomical and Space Sciences
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 5106 Nuclear and plasma physics
- 5101 Astronomical sciences
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0201 Astronomical and Space Sciences