Exact solution for three particles interacting via zero-range potentials

Journal Article · Wed Mar 15 04:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20786910

Macek, J H; Yu Ovchinnikov, S; Gasaneo, G ^[1]

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1. Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996-1501, USA and Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States)

Exact solutions for three identical bosons interacting via zero-range s-wave potentials are derived. The solutions are contour integrals over a product of hyperradial Bessel functions times angular functions weighted by a coefficient. The product function is a solution of the free-particle Schroedigner equation and the weight function is chosen to satisfy the zero-range boundary conditions. Scattering matrix elements for boson-dimer elastic scattering, breakup of a dimer into three particles and the time-reversed recombination process are derived. For vanishing total energy E, these quantities are given as closed-form functions of the two-body s-wave scattering length a and a three-body renormalization constant R{sub 0}. The exact results obtained by this method are compared with those obtained using other methods. Differences in the functional dependence on R{sub 0} of the order of 2% are noted. Comparison with the hidden-crossing theory finds similar agreement with the functional dependence upon a and R{sub 0}.

• OSTI ID: 20786910
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BESSEL FUNCTIONS
BOSONS
BOUNDARY CONDITIONS
COMPARATIVE EVALUATIONS
DIMERS
ELASTIC SCATTERING
EXACT SOLUTIONS
INTEGRALS
MATRIX ELEMENTS
POTENTIALS
RECOMBINATION
RENORMALIZATION
S MATRIX
S WAVES
SCATTERING LENGTHS
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
TWO-BODY PROBLEM
WEIGHTING FUNCTIONS