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 $2\to 2,3$ 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 e+−e^+ -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 $e^+ e^-$ annihilation amplitude, the amplitude of Positronium formation and respective cross sections. A number of $e^+ e^-$ direct annihilation cross sections and Positronium formation cross sections in the energy gap between Ps$(1s)$ and H$(n=2)$ 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 $n-{^3}$H, $n-{^3}$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-$^3$He and p-$^3$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$_3$ 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