Accumulation of three-body resonances above two-body thresholds

Abstract

We calculate resonances in three-body systems with attractive Coulomb potentials by solving the homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved by using the Coulomb-Sturmian separable expansion approach. This approach provides an exact treatment of the threshold behavior of the three-body Coulombic systems. We considered the negative positronium ion and, besides locating all the previously know $S$-wave resonances, we found a whole bunch of new resonances accumulated just slightly above the two-body thresholds. The way they accumulate indicates that probably there are infinitely many resonances just above the two-body thresholds, and this might be a general property of three-body systems with attractive Coulomb potentials.

arXiv comment4 pages, 3 figures

References in corpus (4)

• Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions
• Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials
• Induced long range dipole field enhanced antihydrogen formation in the $\bar{p}+Ps(n=2)\to e^{-}+\bar{H}(n\le 2)$ reaction
• Faddeev-Merkuriev equations for resonances in three-body Coulombic systems

Cited by in corpus (9)

• On the Calculation of Resonances in Pre-Born-Oppenheimer Molecular Structure Theory
• On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
• Green's operator for Hamiltonians with Coulomb plus polynomial potentials
• Universality of excited three-body bound states in one dimension
• Geometric scaling in the spectrum of an electron captured by a stationary finite dipole
• Some applications of the Faddeev-Yakubovsky equations to the cold-atom physics
• Faddeev-Merkuriev integral equations for atomic three-body resonances
• Charged three-body system with arbitrary masses near conformal invariance
• Series of broad resonances in atomic three-body systems