Singular Short Range Potentials in the J-Matrix Approach

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.

14 pages, 5 tables, 2 figures

References in corpus (8)

• Reentrant transitions in colloidal or dusty plasma bilayers
• The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states
• An extended class of L2-series solutions of the wave equation
• Exact method for locating potential resonances and Regge trajectories
• The generalized pseudospectral approach to the bound states of Hulthen and Yukawa potentials
• Pade approximation of the S-matrix as a way of locating quantum resonances and bound states
• The rotating Morse potential model for diatomic molecules in the J-matrix representation: II. The S-matrix approach
• Unified algebraic treatment of resonance

Cited by in corpus (5)

• Extending the class of solvable potentials: II. Screened Coulomb potential with a barrier
• Analytical Treatment of the Oscillating Yukawa Potential
• J-matrix method of scattering for inverse-square singular potential with supercritical coupling I. Theory
• Energy spectrum of a generalized Scarf potential using the Asymptotic Iteration Method and the Tridiagonal Representation Approach
• J-matrix method of scattering for potentials with inverse square singularity: The real representation