The 3-body Coulomb problem

Abstract

We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived from the consideration of the scattering properties of the system. In particular this makes full use of the solution of the two-body problem, the interaction appearing only through the corresponding known T-matrix. In the case of the Coulomb potential we make use of a very convenient expression for the T-matrix obtained by Schwinger. As a check we apply this approach to the well-known problem of the Helium atom ground state and obtain a perfect numerical agreement with the known result for the ground state energy. The wave function is directly obtained from the corresponding solution. We expect our method to be in particular quite useful for the trion problem in semiconductors.

19 pages, 8 figures

References in corpus (11)

• Theory of ultracold Fermi gases
• Universal few-body physics and cluster formation
• Few-body physics with ultracold atomic and molecular systems in traps
• Nucleon-Deuteron Scattering from an Effective Field Theory
• Virial expansion for a strongly correlated Fermi gas
• Efimov Resonances in Ultracold Quantum Gases
• Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Bound states of three and four resonantly interacting particles
• Trion ground state, excited states and absorption spectrum using electron-exciton basis
• The Coulomb Green's Function in Two Dimensions

Cited by in corpus (9)

• Fermion Pair Dynamics in Open Quantum Systems
• Microscopic description of exciton-polaritons in microcavities
• Microscopic calculation of polariton scattering in semiconductor microcavities
• Enhanced scattering between electrons and exciton-polaritons in a microcavity
• Trion resonance in polariton-electron scattering
• Trion ground state energy: simple results
• Efficient calculation of trion energies in monolayer transition metal dichalcogenides
• Quantum Monte Carlo study of three-dimensional Coulomb complexes: trions and biexcitons; hydrogen molecules and ions; helium hydride cations; and positronic and muonic complexes
• Atom-dimer and dimer-dimer scatterings in a spin-orbit coupled Fermi gas