s-Wave resonance in exponential cosine screened Coulomb potential

Abstract

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 $\lambda _{\mathrm{c}} = 0.720524$ 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 $\lambda _{\mathrm{r}}^{+} = 0.90035$. The behavior of the system in the gap $\lambda _{\mathrm{c}}< \lambda < \lambda _{\mathrm{r}}^{+}$ 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 $\lambda _{\mathrm{r}}^{+}$, 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.

Graphic Abstract