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 |
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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 | |
Publication status | Published - Jun 29 2009 |
Keywords
- Bound states
- Critical screening
- J-matrix method
- Resonances
- Singular short-range potential
ASJC Scopus subject areas
- General Physics and Astronomy