Singular short range potentials in the J-matrix approach

M. S. Abdelmonem; I. Nasser; H. Bahlouli; U. Al Khawaja; A. D. Alhaidari

doi:10.1016/j.physleta.2009.05.012

Singular short range potentials in the J-matrix approach

M. S. Abdelmonem
, I. Nasser
, H. Bahlouli^*
, U. Al Khawaja
, A. D. Alhaidari

^*Corresponding author for this work

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

15 Scopus citations

Abstract

We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1 / r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.

Original language	English
Pages (from-to)	2408-2412
Number of pages	5
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	373
Issue number	29
DOIs	https://doi.org/10.1016/j.physleta.2009.05.012
State	Published - 29 Jun 2009

Bibliographical note

Funding Information:
The authors acknowledge the support provided by the Physics department at King Fahd University of Petroleum & Minerals under project FT-080010. We are also grateful to “Khaled Technical & Commercial Services” (KTeCS) for the generous support.

Keywords

Bound states
Critical screening
J-matrix method
Resonances
Singular short-range potential

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.physleta.2009.05.012

Cite this

@article{86aff432124b4af9bca39a04fe4a7183,

title = "Singular short range potentials in the J-matrix approach",

abstract = "We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1 / r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.",

keywords = "Bound states, Critical screening, J-matrix method, Resonances, Singular short-range potential",

author = "Abdelmonem, \{M. S.\} and I. Nasser and H. Bahlouli and \{Al Khawaja\}, U. and Alhaidari, \{A. D.\}",

note = "Funding Information: The authors acknowledge the support provided by the Physics department at King Fahd University of Petroleum \& Minerals under project FT-080010. We are also grateful to “Khaled Technical \& Commercial Services” (KTeCS) for the generous support. ",

year = "2009",

month = jun,

day = "29",

doi = "10.1016/j.physleta.2009.05.012",

language = "English",

volume = "373",

pages = "2408--2412",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

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T1 - Singular short range potentials in the J-matrix approach

AU - Abdelmonem, M. S.

AU - Nasser, I.

AU - Bahlouli, H.

AU - Al Khawaja, U.

AU - Alhaidari, A. D.

N1 - Funding Information: The authors acknowledge the support provided by the Physics department at King Fahd University of Petroleum & Minerals under project FT-080010. We are also grateful to “Khaled Technical & Commercial Services” (KTeCS) for the generous support.

PY - 2009/6/29

Y1 - 2009/6/29

N2 - We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1 / r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.

AB - We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1 / r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.

KW - Bound states

KW - Critical screening

KW - J-matrix method

KW - Resonances

KW - Singular short-range potential

UR - https://www.scopus.com/pages/publications/67349221791

U2 - 10.1016/j.physleta.2009.05.012

DO - 10.1016/j.physleta.2009.05.012

M3 - Article

AN - SCOPUS:67349221791

SN - 0375-9601

VL - 373

SP - 2408

EP - 2412

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

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

IS - 29

ER -

Singular short range potentials in the J-matrix approach

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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