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Register a new userFaddeev-Merkuriev equations for resonances in three-body Coulombic systems
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We reconsider the homogeneous Faddeev-Merkuriev integral equations for three-body Coulombic systems with attractive Coulomb interactions and point out that the resonant solutions are contaminated with spurious resonances. The spurious solutions are related to the splitting of the attractive Coulomb potential into short- and long-range parts, which is inherent in the approach, but arbitrary to some extent. By varying the parameters of the splitting the spurious solutions can easily be ruled out. We solve the integral equations by using the Coulomb-Sturmian separable expansion approach. This solution method provides an exact description of the threshold phenomena. We have found several new S-wave resonances in the e- e+ e- system in the vicinity of thresholds.
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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 Greens operator has been calculated as a contour integral of two-body Coulomb Greens 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
A novel method for calculating resonances in three-body Coulombic systems is proposed. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. The $e^- e^+ e^-$ S-state resonances up to $n=5$ threshold are calculated.
A novel method for calculating resonances in three-body Coulombic systems is presented. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. To show the power of the method we calculate resonances of the three-$alpha$ and the $H^-$ systems.
We propose a novel method for calculating resonances in three-body Coulombic systems. The method is based on the solution of the set of Faddeev and Lippmann-Schwinger integral equations, which are designed for solving the three-body Coulomb problem. The resonances of the three-body system are defined as the complex-energy solutions of the homogeneous Faddeev integral equations. We show how the kernels of the integral equations should be continued analytically in order that we get resonances. As a numerical illustration a toy model for the three-$alpha$ system is solved.
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.
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