From Two-Body Resonances to Three-Body Borromean States

Abstract

In this work we use the complex-scaled hyperspheric adiabatic expansion method to investigate the spectrum of three-body systems. This method provides a description of not only bound states, but also three-body resonances. We first consider the case of an infinitely heavy core and two non-interacting light particles. When each of the core-particle subsystems shows a resonance, the three-body state presents a three-body resonance with energy equal to the sum of the two two-body resonance energies. When one of the core-particle subsystems has a virtual s-state the sum of the two two-body energies does not correspond to a three-body resonance, but to a virtual state of the same energy relative to the resonant two-body system. The effects produced by the motion of the two-body centre of masses when the mass of the core is made finite are also investigated. Calculations including an interaction between particles 2 and 3 are also considered. We show how these effects can lead to the appearance of Borromean three-body states.