Origin of three-body resonances

Abstract

We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the $S$-matrix. For one infinitely heavy core and two non-interacting light particles, the complex energies of the three-body poles are the sum of the two two-body complex pole-energies. These generic relations are modified by center-of-mass effects which alone can produce a Borromean system. We show how the three-body states evolve in ${}^6$He, ${}^6$Li, and ${}^6$Be when the nucleon-nucleon interaction is continuously switched on. The schematic model is able to reproduce the main properties in their spectra. Realistic calculations for these nuclei are shown in detail for comparison. The implications of a core with non-zero spin are investigated and illustrated for ${}^{17}$Ne (${}^{15}$O+p+p). Dimensionless units allow predictions for systems of different scales.

15 pages, 7 figures

References in corpus (21)

• Gamow Shell Model Description of Neutron-Rich Nuclei
• Study of bound and scattering states in three-nucleon systems
• The structure of the atomic helium trimers: Halos and Efimov states
• Testing Non-local Nucleon-Nucleon Interactions in the Four-Nucleon Systems
• Three-body resonances in He-6, Li-6, and Be-6, and the soft dipole mode problem of neutron halo nuclei
• Three-body structure of the low-lying ${}^{17}$Ne-states
• Shell model in the complex energy plane and two-particle resonances
• Complex scaling of the hyper-spheric coordinates and Faddeev equations
• The simplest ``strange'' three-body halo
• Three-body resonances by complex scaling
• Three-body Thomas-Ehrman shifts of analog states of ${}^{17}$Ne and ${}^{17}$N
• Phase equivalent potentials for three-body halos
• Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials
• Three-boson relativistic bound states with zero-range interaction
• Resonances in the three-neutron system
• Spin-dependent effective interactions for halo nuclei
• Comprehensive calculations of three--body breakup cross sections
• Virtual states of light non-Borromean halo nuclei
• Anatomy of three-body decay II. Decay mechanism and resonance structure
• Complex Scaling of the Faddeev Operator
• Origin of Borromean systems

Cited by in corpus (3)

• Above threshold s-wave resonances illustrated by the 1/2${}^{+}$ states in ${}^9$Be and ${}^9$B
• Neutron-${}^3$H potentials and the ${}^5$H-properties
• Universality of excited three-body bound states in one dimension