2,435 research outputs found
Variational separable expansion scheme for two-body Coulomb-scattering problems
We present a separable expansion approximation method for Coulomb-like
potentials which is based on Schwinger variational principle and uses
Coulomb-Sturmian functions as basis states. The new scheme provides faster
convergence with respect to our formerly used non-variational approach.Comment: some typos correcte
Electron-hydrogen scattering in Faddeev-Merkuriev integral equation approach
Electron-hydrogen scattering is studied in the Faddeev-Merkuriev integral
equation approach. The equations are solved by using the Coulomb-Sturmian
separable expansion technique. We present - and -wave scattering and
reactions cross sections up to the threshold.Comment: 2 eps figure
On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis,
has an infinite symmetric tridiagonal form, also known as Jacobi matrix form.
This Jacobi matrix structure involves a continued fraction representation for
the inverse of the Green's matrix. The continued fraction can be transformed to
a ratio of two hypergeometric functions. From this result we find
an exact analytic formula for the matrix elements of the Green's operator of
the Coulomb Hamiltonian.Comment: 8 page
Three-potential formalism for the atomic three-body problem
Based on a three-potential formalism we propose mathematically well-behaved
Faddeev-type integral equations for the atomic three-body problem and descibe
their solutions in Coulomb-Sturmian space representation. Although the system
contains only long-range Coulomb interactions these equations allow us to reach
solution by approximating only some auxiliary short-range type potentials. We
outline the method for bound states and demonstrate its power in benchmark
calculations. We can report a fast convergence in angular momentum channels.Comment: considerably revised, 9 pages, revtex, 1 ps figur
Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials
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 S-state
resonances up to threshold are calculated.Comment: 6 pages, 2 ps figure
Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal
(Jacobi) matrix form in some discrete Hilbert-space basis representation, then
its Green's operator can be constructed in terms of a continued fraction. As an
illustrative example we discuss the Coulomb Green's operator in
Coulomb-Sturmian basis representation. Based on this representation, a quantum
mechanical approximation method for solving Lippmann-Schwinger integral
equations can be established, which is equally applicable for bound-, resonant-
and scattering-state problems with free and Coulombic asymptotics as well. The
performance of this technique is illustrated with a detailed investigation of a
nuclear potential describing the interaction of two particles.Comment: 7 pages, 4 ps figures, revised versio
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