Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions

Abstract

A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into a two-body single channel, a two-body multichannel and a genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve them by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the $e^{+}+H$ system both below and above the $H(n=2)$ threshold. We found excellent agreements with previous calculations in most cases.

12 pages, 3 figures

References in corpus (5)

• Coulomb-Sturmian separable expansion approach: Three-body Faddeev calculations for Coulomb-like interactions
• Three-potential formalism for the three-body Coulomb scattering problem
• Green's matrix from Jacobi-matrix Hamiltonian
• Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states
• Three-potential formalism for the atomic three-body problem

Cited by in corpus (19)

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• Three-body calculation of the $1s$ level shift in kaonic deuterium with realistic $\bar{K}N$ potentials
• Three-body breakup within the fully discretized Faddeev equations
• On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
• Three-body calculation of the $1s$ level shift in kaonic deuterium
• Electron-hydrogen scattering in Faddeev-Merkuriev integral equation approach
• Discrete Wave-Packet Representation in Nuclear Matter Calculations
• Faddeev-Merkuriev equations for resonances in three-body Coulombic systems
• Green's operator for Hamiltonians with Coulomb plus polynomial potentials
• Some applications of the Faddeev-Yakubovsky equations to the cold-atom physics
• Theoretical study of reactions in the three body $e^{-}{e}^{+}\bar{p}$ system and antihydrogen formation cross sections
• Treatment of confinement in the Faddeev approach to three-quark problems
• Faddeev-Merkuriev integral equations for atomic three-body resonances
• Application of the complex scaling method in quantum scattering theory
• Application of the complex scaling method in solving three-body Coulomb scattering problem
• Calculation of Relativistic Single-Particle States