# Bound states of three and four resonantly interacting particles

Research paper by I. V. Brodsky, A. V. Klaptsov, M. Yu. Kagan, R. Combescot, X. Leyronas

Indexed on: 24 Nov '05Published on: 24 Nov '05Published in: Physics - Strongly Correlated Electrons

#### 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\$.