Exact diagrammatic approach for dimerdimer scattering and bound states of three and four resonantly interacting particles
Abstract
We present a diagrammatic approach for the dimerdimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimerdimer scattering length a{sub B} in three spatial dimensions, for dimers made of two fermions in a spinsinglet state, with corresponding scattering length a{sub F}, and the already known result a{sub B}=0.60 a{sub F} is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate boundstate energies for three bbb and four bbbb resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact boundstate energies of two bosons plus one fermion bbf, two bosons plus two fermions bf{sub {up_arrow}}bf{sub {down_arrow}}, and three bosons plus one fermion bbbf.
 Authors:
 P.L. Kapitza Institute for Physical Problems, Kosygin street 2, Moscow, Russia, 119334 (Russian Federation)
 (Russian Federation)
 (France)
 Publication Date:
 OSTI Identifier:
 20786930
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.032724; (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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSEEINSTEIN CONDENSATION; BOSONS; BOUND STATE; DIMERS; FERMIONS; INTERACTING BOSON MODEL; RESONANCE; SCATTERING; SCATTERING LENGTHS; SPIN
Citation Formats
Brodsky, I. V., Kagan, M. Yu., Klaptsov, A. V., Combescot, R., Leyronas, X., Russian Research Centre 'Kurchatov Institute', Kurchatov square 1, Moscow, Russia, 123182, and Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05. Exact diagrammatic approach for dimerdimer scattering and bound states of three and four resonantly interacting particles. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.
Brodsky, I. V., Kagan, M. Yu., Klaptsov, A. V., Combescot, R., Leyronas, X., Russian Research Centre 'Kurchatov Institute', Kurchatov square 1, Moscow, Russia, 123182, & Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05. Exact diagrammatic approach for dimerdimer scattering and bound states of three and four resonantly interacting particles. United States. doi:10.1103/PHYSREVA.73.0.
Brodsky, I. V., Kagan, M. Yu., Klaptsov, A. V., Combescot, R., Leyronas, X., Russian Research Centre 'Kurchatov Institute', Kurchatov square 1, Moscow, Russia, 123182, and Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05. Wed .
"Exact diagrammatic approach for dimerdimer scattering and bound states of three and four resonantly interacting particles". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20786930,
title = {Exact diagrammatic approach for dimerdimer scattering and bound states of three and four resonantly interacting particles},
author = {Brodsky, I. V. and Kagan, M. Yu. and Klaptsov, A. V. and Combescot, R. and Leyronas, X. and Russian Research Centre 'Kurchatov Institute', Kurchatov square 1, Moscow, Russia, 123182 and Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05},
abstractNote = {We present a diagrammatic approach for the dimerdimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimerdimer scattering length a{sub B} in three spatial dimensions, for dimers made of two fermions in a spinsinglet state, with corresponding scattering length a{sub F}, and the already known result a{sub B}=0.60 a{sub F} is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate boundstate energies for three bbb and four bbbb resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact boundstate energies of two bosons plus one fermion bbf, two bosons plus two fermions bf{sub {up_arrow}}bf{sub {down_arrow}}, and three bosons plus one fermion bbbf.},
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}
}

Lowenergy properties of three resonantly interacting particles
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Effective interaction of three resonantly interacting particles and the force range
The effect of the force range [ital r][sub 0] on an effective longrange interaction in a system of three resonantly interacting particles is considered. By employing a boundarycondition approach, it is explicitly shown that the account of the force range gives rise to a correction [ital r][sub 0]/[ital R][sup 3] in the effective longrange interaction. The correction is universal (i.e., independent of detail structure of the force), and is attractive for symmetric 0[sup +] threeparticle states. The effect of the correction on the wellknown correlation between the threeparticle binding energy and the particlepair scattering length is calculated.