Exact solution for three particles interacting via zerorange potentials
Abstract
Exact solutions for three identical bosons interacting via zerorange swave 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 freeparticle Schroedigner equation and the weight function is chosen to satisfy the zerorange boundary conditions. Scattering matrix elements for bosondimer elastic scattering, breakup of a dimer into three particles and the timereversed recombination process are derived. For vanishing total energy E, these quantities are given as closedform functions of the twobody swave scattering length a and a threebody 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 hiddencrossing theory finds similar agreement with the functional dependence upon a and R{sub 0}.
 Authors:
 Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 379961501, USA and Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States)
 (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; THREEBODY PROBLEM; TWOBODY 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 zerorange 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 zerorange 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 zerorange potentials". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20786910,
title = {Exact solution for three particles interacting via zerorange 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 zerorange swave 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 freeparticle Schroedigner equation and the weight function is chosen to satisfy the zerorange boundary conditions. Scattering matrix elements for bosondimer elastic scattering, breakup of a dimer into three particles and the timereversed recombination process are derived. For vanishing total energy E, these quantities are given as closedform functions of the twobody swave scattering length a and a threebody 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 hiddencrossing 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}
}

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