skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Exact solution for three particles interacting via zero-range potentials

Abstract

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}.

Authors:
; ;  [1];  [2]
  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)
  2. (8000) Bahia Blanca, Buenos Aires (Argentina)
Publication Date:
OSTI Identifier:
20786910
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.032704; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Macek, J. H., Yu Ovchinnikov, S., Gasaneo, G., and Departamento de Fisica, Universidad Nacional del Sur, Av. Alem1253. Exact solution for three particles interacting via zero-range potentials. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Macek, J. H., Yu Ovchinnikov, S., Gasaneo, G., & Departamento de Fisica, Universidad Nacional del Sur, Av. Alem1253. Exact solution for three particles interacting via zero-range potentials. United States. doi:10.1103/PHYSREVA.73.0.
Macek, J. H., Yu Ovchinnikov, S., Gasaneo, G., and Departamento de Fisica, Universidad Nacional del Sur, Av. Alem1253. Wed . "Exact solution for three particles interacting via zero-range potentials". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786910,
title = {Exact solution for three particles interacting via zero-range potentials},
author = {Macek, J. H. and Yu Ovchinnikov, S. and Gasaneo, G. and Departamento de Fisica, Universidad Nacional del Sur, Av. Alem1253},
abstractNote = {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}.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}