Faddeev-Merkuriev integral equations for atomic three-body resonances
S Keller, A Marotta, Z Papp
TL;DR
This paper develops a method to calculate atomic three-body resonances using Faddeev-Merkuriev integral equations and Coulomb-Sturmian basis, enabling precise determination of complex resonance energies.
Contribution
It introduces a novel approach to solve three-body Coulomb problems by approximating potential terms with Coulomb-Sturmian functions and computing Green's operators via contour integrals.
Findings
Calculated resonances of the e-Ps system at higher energies.
Determined resonances for total angular momentum L=1 with various parities.
Validated the method by locating complex energies as zeros of the Fredholm determinant.
Abstract
Three-body resonances in atomic systems are calculated as complex-energy solutions of Faddeev-type integral equations. The homogeneous Faddeev-Merkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Green's operator has been calculated as a contour integral of two-body Coulomb Green's matrices. This approximation casts the integral equation into a matrix equation and the complex energies are located as the complex zeros of the Fredholm determinant. We calculated resonances of the e-Ps system at higher energies and for total angular momentum L=1 with natural and unnatural parity
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