Singular short range potentials in the J-matrix approach

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

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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 languageEnglish
Pages (from-to)2408-2412
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number29
Publication statusPublished - Jun 29 2009


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

ASJC Scopus subject areas

  • General Physics and Astronomy


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