Faddeev Equations for Atomic Problems. IV. Convergence of the Separable-Expansion Method for Low-Energy Positron-Hydrogen Problems

1971 ◽  
Vol 3 (2) ◽  
pp. 568-573 ◽  
Author(s):  
Paul J. Kramer ◽  
Joseph C. Y. Chen
Keyword(s):  
Expansion Method ◽  
Low Energy ◽  
Faddeev Equations ◽  
Separable Expansion

On the solution of the three-particle integral equations by the separable expansion method

1970 ◽  
Vol 32 (1) ◽  
pp. 19-22 ◽  
Author(s):  
V.F. Kharchenko ◽  
N.M. Petrov ◽  
V.E. Kuzmichev
Keyword(s):  
Integral Equations ◽  
Expansion Method ◽  
Separable Expansion

scholarly journals IMPROVED THERMAL SCATTERING DATA PREPARATION

2021 ◽  
Vol 247 ◽  
pp. 09027
Author(s):  
Amelia Trainer ◽  
Benoit Forget ◽  
Jeremy Conlin
Keyword(s):  
Phonon Frequency ◽  
Expansion Method ◽  
Nuclear Data ◽  
Difficult Problem ◽  
Low Energy ◽  
Scattering Data ◽  
Data Preparation ◽  
Convolution Integrals ◽  
Nuclear Systems ◽  
Scattering Kernel

Convenient access to accurate nuclear data, particularly data describing low-energy neutrons, is crucial for trustworthy simulations of thermal nuclear systems. Obtaining the scattering kernel for thermal neutrons (i.e., neutrons with energy ~1 eV or less) can be a difficult problem, since the neutron energy is not sufficient to break molecular bonds, and thus the neutrons must often interact with a much larger structure. The “scattering law” S(α; β), which is a function of unitless momentum α and energy β transfer, is used to relate the material’s phonon frequency distribution to the scattering kernel. LEAPR (a module of NJOY) and GASKET are two nuclear data processing codes that can be used to prepare the scattering law and use different approaches to approximate the same equations. LEAPR uses the “phonon expansion method” which involves iterative convolution. Iteratively solving convolution integrals is an expensive calculation to perform (to ease this calculation, LEAPR uses trapezoidal integration for the convolution). GASKET uses a more direct approach that, while avoiding the iterative convolutions, can become numerically unstable for some α; β combinations. When both methods are properly converged, they tend to agree quite well. The agreement and departure from agreement is presented here.

scholarly journals Solution of Faddeev integral equations in configuration space using the hyperspherical harmonics expansion method

2014 ◽  
Vol 23 (11) ◽  
pp. 1450069
Author(s):  
Valery I. Kovalchuk
Keyword(s):  
Configuration Space ◽  
Magnetic Moments ◽  
Expansion Method ◽  
Bound State ◽  
Binding Energies ◽  
Hyperspherical Harmonics ◽  
Faddeev Equations ◽  
Charge Radii ◽  
Mixed Symmetry ◽  
Hyperspherical Harmonics Expansion

In this paper, a method has been developed to solve three-particle Faddeev equations in the configuration space making use of a series expansion in hyperspherical harmonics. The following parameters of the bound state of triton and helium-3 nuclei have been calculated: the binding energies, the weights of symmetric and mixed-symmetry components of the wave function, the magnetic moments, and the charge radii.

Quality of the three-nucleon bound-state wave function from a two-nucleon separable expansion method

1991 ◽  
Vol 11 (2-3) ◽  
pp. 89-98 ◽  
Author(s):  
W. C. Parke ◽  
Y. Koike ◽  
D. R. Lehman ◽  
L. C. Maximon
Keyword(s):  
Wave Function ◽  
Expansion Method ◽  
Bound State ◽  
State Wave ◽  
Bound State Wave Function ◽  
Separable Expansion

Stringent tests of the potential separable expansion method

1988 ◽  
Vol 64 (1-3) ◽  
pp. 247-253
Author(s):  
B. Gyarmati ◽  
A. T. Kruppa ◽  
Z. Papp
Keyword(s):  
Expansion Method ◽  
Separable Expansion
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