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.
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All relevant data are included in the paper.]
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Acknowledgements
The authors would like to thank Prof. H. Hogreve for helpful discussions on the one-dimensional model potential and the two anonymous reviewers for their valuable comments and suggestions. Financial support from the National Natural Science Foundation of China (Grant Nos. 12174147, 11774131, and 91850114) is greatly acknowledged.
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All the authors were involved in the preparation of the manuscript and have read and approved the final version. LGJ and AL initiated the project and wrote the manuscript. XHJ and ZXH ran the program and generated the data. HEM and YKH carried out the analysis of results and significantly improved the manuscript.
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Jiao, L.G., Ji, X.H., Hu, Z.X. et al. s-Wave resonance in exponential cosine screened Coulomb potential. Eur. Phys. J. D 75, 313 (2021). https://doi.org/10.1140/epjd/s10053-021-00330-1
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DOI: https://doi.org/10.1140/epjd/s10053-021-00330-1