Alternative to Pade technique for solving scattering integral equations

Journal Article · Wed Jul 01 04:00:00 EDT 1981 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.24.43· OSTI ID:6379694

Tomio, L; Adhikari, S K

The aim of this work is to show how we can improve systematically the rate of convergence of a recently proposed method for iterative solution of scattering integral equations. The method relies on the introduction of an auxiliary equation containing an arbitrary function, whose kernel is much weaker than that of the original equation. The solution of the original equation is then expressed in terms of that of the auxiliary equation which is supposed to have a convergent iterative solution. In this work we introduce successive subtractions in the kernel in order to make it weaker. Such subtractions in the kernel are very simple to implement in practice and the present method appears to have some advantage over the other existing methods. We explain how to generalize the method for multichannel scattering equations. Using the present method we show how to modify a method by Fuda for three-particle scattering equations in order to have a method which uses the iterative solution only of nonsingular equations above the three-body breakup threshold. The method is used numerically to compute phase shifts, scattering lengths, and fully off-shell t matrix elements for neutron-deuteron scattering in the s-wave Amado model and for nucleon-nucleon scattering with the Reid /sup 1/S/sub 0/ potential. The iterative solution of the auxiliary equation is found to converge much faster than the conventional Pade technique in the case of the neutron-deuteron scattering and yields results with high precision.

• Research Organization: Departamento de Fisica, Universidade Federal de Pernambuco, 50.000-Recife, Pe., Brazil
• OSTI ID: 6379694
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Journal Issue: 1 Vol. 24:1; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

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A=1-5
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653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BARYON REACTIONS
DEUTERIUM TARGET
DIMENSIONS
EQUATIONS
HADRON REACTIONS
INTEGRAL EQUATIONS
ITERATIVE METHODS
LENGTH
LIPPMANN-SCHWINGER EQUATION
MANY-BODY PROBLEM
MATRICES
MATRIX ELEMENTS
NEUTRON REACTIONS
NUCLEAR REACTIONS
NUCLEON REACTIONS
NUCLEON-NUCLEON POTENTIAL
PHASE SHIFT
POTENTIALS
REID POTENTIAL
S MATRIX
SCATTERING LENGTHS
TARGETS
THREE-BODY PROBLEM