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arXiv · 1010.1844

Singular Short Range Potentials in the J-Matrix Approach

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

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M. S. Abdelmonem, I. Nasser, H. Bahlouli, U. Al-Khawaja, A. D. Alhaidari. 2010-10-09. Singular Short Range Potentials in the J-Matrix Approach. https://doi.org/10.1016/j.physleta.2009.05.012

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