167 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
Unified treatment of the Coulomb and harmonic oscillator potentials in dimensions
Quantum mechanical models and practical calculations often rely on some
exactly solvable models like the Coulomb and the harmonic oscillator
potentials. The dimensional generalized Coulomb potential contains these
potentials as limiting cases, thus it establishes a continuous link between the
Coulomb and harmonic oscillator potentials in various dimensions. We present
results which are necessary for the utilization of this potential as a model
and practical reference problem for quantum mechanical calculations. We define
a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate
the Green's operator on this basis and also present an SU(1,1) algebra
associated with it. We formulate the problem for the one-dimensional case too,
and point out that the complications arising due to the singularity of the
one-dimensional Coulomb problem can be avoided with the use of the generalized
Coulomb potential.Comment: 18 pages, 3 ps figures, revte
Calculation of Relativistic Single-Particle States
A computational method is proposed to calculate bound and resonant states by
solving the Klein-Gordon and Dirac equations for real and complex energies,
respectively. The method is an extension of a non-relativistic one, where the
potential is represented in a Coulomb-Sturmian basis. This basis facilitates
the exact analytic evaluation of the Coulomb Green's operator in terms of a
continued fraction. In the extension to relativistic problems, we cast the
Klein-Gordon and Dirac equations into an effective Schr\"odinger form. Then the
solution method is basically an analytic continuation of non-relativistic
quantities like the angular momentum, charge, energy and potential into the
effective relativistic counterparts.Comment: 10 page
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
Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions
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 system both below
and above the threshold. We found excellent agreements with previous
calculations in most cases.Comment: 12 pages, 3 figure
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
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
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