Physical Review A

Unitary interaction geometries in few-body systems

Lorenzo Contessi, Johannes Kirscher, Manuel Pavón Valderrama

Published Mar 19, 2024• 1 citation

Abstract

We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a unitary graph in which the vertices represent distinguishable particles and the edges resonant two-body interactions. Few-body systems whose unitary graph is connected will collapse unless a repulsive three-body interaction is included. We find two categories of graphs, distinguished by the kind of three-body repulsion necessary to stabilize the associated system. Each category is characterized by whether the graph contains a loop or not: for tree-like graphs (graphs containing a loop) the three-body force renormalizing them is the same as in the three-body system with two (three) resonant interactions. We show numerically that this conjecture is correct for the four-body case as well as for a few five-body configurations. We explain this result in the four-body sector qualitatively by imposing Bethe-Peierls boundary conditions on the pertinent Faddeev-Yakubovsky decomposition of the wave function.

DOI: 10.1103/physreva.109.032217

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