Three-body scattering from nonperturbative flow equations

Journal Article · Mon Sep 15 04:00:00 EDT 2008 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.78.034001· OSTI ID:21192179

Diehl, S ^[1]; Krahl, H C; Scherer, M ^[2]

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1. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)
2. Institut fuer Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg (Germany)

We consider fermion-dimer scattering in the presence of a large positive scattering length in the frame of functional renormalization group equations. A flow equation for the momentum dependent fermion-dimer scattering amplitude is derived from first principles in a systematic vertex expansion of the exact flow equation for the effective action. The resummation obtained from the nonperturbative flow is shown to be equivalent to the one performed by the integral equation by Skorniakov and Ter-Martirosian (STM). The flow equation approach allows to integrate out fermions and bosons simultaneously, in line with the fact that the bosons are not fundamental but build up gradually as fluctuation induced bound states of fermions. In particular, the STM result for atom-dimer scattering is obtained by choosing the relative cutoff scales of fermions and bosons such that the fermion fluctuations are integrated out already at the initial stage of the RG evolution.

• OSTI ID: 21192179
• Journal Information: Physical Review. C, Nuclear Physics, Journal Name: Physical Review. C, Nuclear Physics Journal Issue: 3 Vol. 78; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ATOMS
BOSONS
BOUND STATE
DIMERS
EVOLUTION
EXPANSION
FERMIONS
FLUCTUATIONS
RENORMALIZATION
SCANNING TUNNELING MICROSCOPY
SCATTERING
SCATTERING AMPLITUDES
SCATTERING LENGTHS
THREE-BODY PROBLEM