Bound states of three and four resonantly interacting particles

I. V. Brodsky; A. V. Klaptsov; M. Yu. Kagan; R. Combescot; X. Leyronas

doi:10.1134/1.2130911

paper

Bound states of three and four resonantly interacting particles

arXiv:cond-mat/0507240 · doi:10.1134/1.2130911

Abstract

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin-singlet state, with corresponding scattering length $a_{F}$ . Applying this approach to the calculation of the dimer-dimer scattering length $a_{B}$ , we recover exactly the already known result $a_{B} = 0.60 a_{F}$ . 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 resonant interaction between fermions and bosons we calculate exactly bound state energies of the following complexes: two bosons plus one fermion $bb f$ , two bosons plus two fermions $b f_{↑} b f_{↓}$ , and three bosons plus one fermion $bbb f$ .

10 pages, 9 figures

Bound states of three and four resonantly interacting particles

Abstract

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