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 -