TY - JOUR

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

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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 -