s-Wave resonance in exponential cosine screened Coulomb potential.

The s-wave resonance in the exponential cosine screened Coulomb potential is investigated by employing the uniform complex-scaling generalized pseudospectral method. It is found that beyond the well-known critical screening parameter λ c = 0.720524 where the ground state merges into the continuum, there exists a huge gap for the screening parameter before the ground state transforms into a well-defined shape resonance lying above the autoionization threshold. The critical value for the emergence of such a shape resonance is determined at about λ r + = 0.90035 . The behavior of the system in the gap λ c < λ < λ r + is still a mystery, and it is conjectured that the bound state would probably transform into negative-energy virtual states and below-threshold shape resonances. For screening parameters larger than λ r + , the resonance positions and widths are calculated with high precision and the results are comparable to previous predictions available in the literature. The trajectories of the poles of S-matrix in both the complex energy and momentum planes are obtained. [ABSTRACT FROM AUTHOR]