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VOLUME 82 | ISSUE 5 | PAGE 306
Bound states of three and four resonantly interacting particles

I. V. Brodsky, A. V. Klaptsov+, M. Yu. Kagan, R. Combescot*, X. Leyronas*
P. L. Kapitza Institute for Physical Problems RAS, 119334 Moscow, Russia [3mm] +Russian Research Centre «Kurchatov Institute", 123182 Moscow, Russia
*Laboratoire de Physique Statistique, Ecole Normale Supérieure, 75231 Paris Cedex 05, France

PACS: 61.72.Cc, 61.80.Az, 61.82.Ms
We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length aF. Applying this approach to the calculation of the dimer-dimer scattering length aB, we recover exactly the already known result aB=0.6 aF. We use the developed approach to obtain new results in 2D for fermions as well as for bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons we calculate exactly bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf_{\uparrow}bf_{\downarrow}, and three bosons plus one fermion bbbf.

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