Regularization in the J-matrix method of scattering revisited

A. D. Alhaidari; H. Bahlouli; M. S. Abdelmonem; F. Al-Ameen; T. Al-Abdulaal

doi:10.1016/j.physleta.2006.12.027

Regularization in the J-matrix method of scattering revisited

A. D. Alhaidari^*
, H. Bahlouli
, M. S. Abdelmonem
, F. Al-Ameen
, T. Al-Abdulaal

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We present an alternative, but equivalent, approach to the regularization of the reference problem in the J-matrix method of scattering. After identifying the regular solution of the reference wave equation with the "sine-like" solution in the J-matrix approach we proceed by direct integration to find the expansion coefficients in an L² basis set that ensures a tridiagonal representation of the reference Hamiltonian. A differential equation in the energy is then deduced for these coefficients. The second independent solution of this equation, called the "cosine-like" solution, is derived by requiring it to pertain to the L² space. These requirements lead to solutions that are exactly identical to those obtained in the classical J-matrix approach. We find the present approach to be more direct and transparent than the classical differential approach of the J-matrix method.

Original language	English
Pages (from-to)	372-377
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	364
Issue number	5
DOIs	https://doi.org/10.1016/j.physleta.2006.12.027
State	Published - 7 May 2007

Bibliographical note

Funding Information:
H. Bahlouli and M.S. Abdelmonem acknowledge the support of King Fahd University of Petroleum and Minerals under project FT-2005/11. Al-Ameen and Al-Abdulaal are grateful to Girls College of Sciences, higher studies section, and the physics department for their support.

Keywords

J-matrix method
Recursion relation
Scattering
Tridiagonal representation

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.physleta.2006.12.027

Cite this

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title = "Regularization in the J-matrix method of scattering revisited",

abstract = "We present an alternative, but equivalent, approach to the regularization of the reference problem in the J-matrix method of scattering. After identifying the regular solution of the reference wave equation with the {"}sine-like{"} solution in the J-matrix approach we proceed by direct integration to find the expansion coefficients in an L2 basis set that ensures a tridiagonal representation of the reference Hamiltonian. A differential equation in the energy is then deduced for these coefficients. The second independent solution of this equation, called the {"}cosine-like{"} solution, is derived by requiring it to pertain to the L2 space. These requirements lead to solutions that are exactly identical to those obtained in the classical J-matrix approach. We find the present approach to be more direct and transparent than the classical differential approach of the J-matrix method.",

keywords = "J-matrix method, Recursion relation, Scattering, Tridiagonal representation",

author = "Alhaidari, \{A. D.\} and H. Bahlouli and Abdelmonem, \{M. S.\} and F. Al-Ameen and T. Al-Abdulaal",

note = "Funding Information: H. Bahlouli and M.S. Abdelmonem acknowledge the support of King Fahd University of Petroleum and Minerals under project FT-2005/11. Al-Ameen and Al-Abdulaal are grateful to Girls College of Sciences, higher studies section, and the physics department for their support. ",

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language = "English",

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T1 - Regularization in the J-matrix method of scattering revisited

AU - Alhaidari, A. D.

AU - Bahlouli, H.

AU - Abdelmonem, M. S.

AU - Al-Ameen, F.

AU - Al-Abdulaal, T.

N1 - Funding Information: H. Bahlouli and M.S. Abdelmonem acknowledge the support of King Fahd University of Petroleum and Minerals under project FT-2005/11. Al-Ameen and Al-Abdulaal are grateful to Girls College of Sciences, higher studies section, and the physics department for their support.

PY - 2007/5/7

Y1 - 2007/5/7

N2 - We present an alternative, but equivalent, approach to the regularization of the reference problem in the J-matrix method of scattering. After identifying the regular solution of the reference wave equation with the "sine-like" solution in the J-matrix approach we proceed by direct integration to find the expansion coefficients in an L2 basis set that ensures a tridiagonal representation of the reference Hamiltonian. A differential equation in the energy is then deduced for these coefficients. The second independent solution of this equation, called the "cosine-like" solution, is derived by requiring it to pertain to the L2 space. These requirements lead to solutions that are exactly identical to those obtained in the classical J-matrix approach. We find the present approach to be more direct and transparent than the classical differential approach of the J-matrix method.

AB - We present an alternative, but equivalent, approach to the regularization of the reference problem in the J-matrix method of scattering. After identifying the regular solution of the reference wave equation with the "sine-like" solution in the J-matrix approach we proceed by direct integration to find the expansion coefficients in an L2 basis set that ensures a tridiagonal representation of the reference Hamiltonian. A differential equation in the energy is then deduced for these coefficients. The second independent solution of this equation, called the "cosine-like" solution, is derived by requiring it to pertain to the L2 space. These requirements lead to solutions that are exactly identical to those obtained in the classical J-matrix approach. We find the present approach to be more direct and transparent than the classical differential approach of the J-matrix method.

KW - J-matrix method

KW - Recursion relation

KW - Scattering

KW - Tridiagonal representation

UR - https://www.scopus.com/pages/publications/33947390837

U2 - 10.1016/j.physleta.2006.12.027

DO - 10.1016/j.physleta.2006.12.027

M3 - Article

AN - SCOPUS:33947390837

SN - 0375-9601

VL - 364

SP - 372

EP - 377

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 5

ER -

Regularization in the J-matrix method of scattering revisited

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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