Precise numerical results for limit cycles in the quantum three-body problem

Journal Article · Sun Jan 15 00:00:00 EST 2006 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2005.10.002· OSTI ID:20766981

Mohr, R F ^[1]; Furnstahl, R J ^[1]; Hammer, H -W ^[2]; Perry, R J ^[1]; Wilson, K G ^[1]

---

1. Department of Physics, Ohio State University, Columbus, OH 43210 (United States)
2. Helmholtz- Institut fuer Strahlen- und Kernphysik (Theorie), Universitaet Bonn, 53115 Bonn (Germany)

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930s. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems (e.g., few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.

• OSTI ID: 20766981
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 321; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
BINDING ENERGY
BOUND STATE
INTERACTIONS
LIMIT CYCLE
NUCLEAR PHYSICS
QUANTUM FIELD THEORY
RENORMALIZATION
THREE-BODY PROBLEM
TWO-BODY PROBLEM