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Bound states of three and four resonantly interacting particles

I. V. Brodsky·A. V. Klaptsov·M. Yu. Kagan·R. Combescot·X. Leyronas
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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 $bbf$, two bosons plus two fermions $bf_{\uparrow}bf_{\downarrow}$, and three bosons plus one fermion $bbbf$.

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I. V. Brodsky, A. V. Klaptsov, M. Yu. Kagan, R. Combescot, X. Leyronas. 2005-11-24. Bound states of three and four resonantly interacting particles. https://doi.org/10.1134/1.2130911

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