1,809 research outputs found
Spectral Properties of Faddeev Equations in Differential Form
Three-body Faddeev equations are considered as a spectral problem for
nonsymmetrical matrix operator. Invariant subspaces related to physical and
spurious solutions to Faddeev equations and its adjoint are described.
Respective eigenvectors corresponding to invariant subspaces are constructed
for Faddeev operator and its adjoint. Extensions of the formalism on CCA
equations are discussed.Comment: LaTeX, Contribution to 16 European Conference on Few-Body Problems in
Physics. Autrans (France) June 1-6 199
The three-body Coulomb scattering problem in discrete Hilbert-space basis representation
For solving the three-body Coulomb scattering problem the
Faddeev-Merkuriev integral equations in discrete Hilbert-space basis
representation are considered. It is shown that as far as scattering amplitudes
are considered the error caused by truncating the basis can be made arbitrarily
small. By this truncation also the Coulomb Green's operator is confined onto
the two-body sector of the three-body configuration space and in leading order
can be constructed with the help of convolution integrals of two-body Green's
operators. For performing the convolution integral an integration contour is
proposed that is valid for all energies, including bound-state as well as
scattering energies below and above the three-body breakup threshold.Comment: Revtex, 8 pages, 1 figure, revised versio
Positron annihilation in H collision above the Positronium formation threshold
A long-standing problem to account for the electron-positron annihilation in
positron Hydrogen scattering above the Positronium formation threshold has been
resolved by the use of the three-body Faddeev formalism. The multichannel
three-body theory for scattering states in presence of a complex absorbing
potential is developed in order to compute the direct annihilation
amplitude, the amplitude of Positronium formation and respective cross
sections. A number of direct annihilation cross sections and
Positronium formation cross sections in the energy gap between Ps and
H thresholds are reported for both the positron-Hydrogen incoming
channel as well as the proton-Positronium incoming channel.Comment: 4 pages, RevTe
Low-energy scattering in four nucleon systems. Method of Cluster Reduction
A method using an expansion of the four-body Yakubovsky wave function
components onto the basis of the Faddeev-equation solutions for the two-cluster
sub-Hamiltonian eigenfunctions is exploited for computations of low-energy
scattering parameters in four nucleon systems. Results of calculations of
low-energy scattering parameters in H, He are presented.Comment: LaTeX, Contribution to 16 European Conference on Few-Body Problems in
Physics. Autrans (France) June 1-6 199
Cluster reduction of the four-body Yakubovsky equations in configuration space for bound-state problem and low-energy scattering
A method using an expansion of the four-body Yakubovsky wave function
components onto the basis of the Faddeev-equation solutions for the two-cluster
sub-Hamiltonian eigenfunctions is proposed. This expansion reduces the
Yakubovsky differential equations to a system of coupled-channel equations for
functions depending on the relative coordinates between the subsystems of the
two-cluster partitions. On the basis of the resulting equations the
four-nucleon bound-state problem and the zero-energy n-t scattering problem are
solved on the relatively small computer.Comment: LaTeX, Submitted to Physics of Atomic Nucle
Calculations of scattering lengths in four-nucleon system on the basis of cluster reduction method for Yakubovsky equations
The cluster reduction method for the Yakubovsky equations in configuration
space is used for calculations of zero-energy scattering in four-nucleon
system. The main idea of the method consists in making use of expansions for
the Yakubovsky amplitudes onto the basis of the Faddeev components for the
two-cluster sub-Hamiltonian eigenfunctions. The expansions reduce the original
equations to ones for the functions depending on the relative coordinates
between the clusters. On the basis of the resulting equations the N-(NNN)
zero-energy scattering problems are solved numerically with the MT I-III model
for N-N forces and neglecting the Coulomb interaction between protons.Comment: LaTeX, 18.4 Kb, Submitted to Physics of Atomic Nuclei. (Revised
version
Computations of scattering lengths in nnpp system within cluster reduction method for Yakubovsky equations
Scattering lengths for d-d, n-He and p-H systems are computed via
Cluster Reduction Method for Yakubovsky equations in configuration space taking
into account Coulomb interaction between protons. MT I-III potential model was
used to describe the nucleon-nucleon interaction. Results of calculations are
in a good agreement with existing experimental data and results of calculations
of other authors.Comment: LaTeX, 5 pages. Contribution to XV International Conference on
Few-Body problem in Physics, Groningen, the Netherlands, 22--26 July 199
Bound State Calculations for Three Atoms Without Explicit Partial Wave Decomposition
A method to calculate the bound states of three-atoms without resorting to an
explicit partial wave decomposition is presented. The differential form of the
Faddeev equations in the total angular momentum representation is used for this
purpose. The method utilizes Cartesian coordinates combined with the
tensor-trick preconditioning for large linear systems and Arnoldi's algorithm
for eigenanalysis. As an example, we consider the He system in which the
interatomic force has a very strong repulsive core that makes the three-body
calculations with standard methods tedious and cumbersome requiring the
inclusion of a large number of partial waves. The results obtained compare
favorably with other results in the field.Comment: 18 pages, 3 figures, 9 tables, revtex
Potential splitting approach to e-H and e-He scattering with zero total angular momentum
An approach based on splitting the reaction potential into a finite range
part and a long range tail part to describe few-body scattering in the case of
a Coulombic interaction is proposed. The solution to the Schr\"odinger equation
for the long range tail of the reaction potential is used as an incoming wave.
This reformulation of the scattering problem into an inhomogeneous
Schr\"odinger equation with asymptotic outgoing waves makes it suitable for
solving with the exterior complex scaling technique. The validity of the
approach is analyzed from a formal point of view and demonstrated numerically,
where the calculations are performed with the finite element method. The method
of splitting the potential in this way is illustrated with calculations of the
electron scattering on the hydrogen atom and the positive helium ion in energy
regions where resonances appear.Comment: 17 pages, 7 figure
Nakupinska redukcija i rješenje zadaće niskoenergijskog raspršenja za nukleonske sustave s N > 3
Cluster reduction method for solution of low-energy scattering problem in few-nucleon system is described. The method reduces the Yakubovsky differential equations to effective equations describing relative motion of clusters. Application of the method to numerical solution of low-energy scattering problem in n-3H, p-3He, n-3He, p-3H and 2H-2H systems are presented.Opisuje se metoda nakupinskog svodenja za rješavanje problema raspršenja sustava s malo nukleona. Metoda svodi Yakubovkove diferencijalne jednadžbe na djelotvorne jednadžbe koje opisuju relativno gibanje nakupina. Predstavljaju se ishodi numeričkog rješavanja zadaće niskoenergijskog raspršenja u sustavima n – 3H, p – 3He, n – 3He, p – 3H i 2H – 2H
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