We present a diagrammatic approach for the dimer-dimer 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 dimer-dimer scattering length a B in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length a F , and the already known result a B = 0.60 a 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 bound-state 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 bound-state energies of two bosons plus one fermion bbf, two bosons plus two fermions bf ↑ bf ↓ , and three bosons plus one fermion bbbf.

We present an exact diagrammatic approach for the dimer-dimer 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 dimer-dimer scattering length aB in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length aF and the already known result aB = 0.60 aF is recovered exactly. Then we make use of our approach to obtain new results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in two dimensions. We consider also the case of resonant interaction between fermions and bosons and we obtain the exact bound state energies of two bosons plus one fermion bbf , two bosons plus two fermions bf ↑ bf ↓ , and three bosons plus one fermion bbbf .

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