Resonances in the Hulthén potential: benchmark calculations, critical behaviors, and interference effects

Abstract

We perform benchmark calculations of resonance states in the Hulthén potential by employing the uniform complex-scaling generalized pseudospectral method. Complex resonance energies for states with the lowest four orbital angular momenta are reported for a wide range of screening parameters where their positions lie above the threshold. Our results are in good agreement with previous J-matrix predictions, but differ significantly from the complex-scaling calculations based on oscillator basis set. By tracing the resonance poles via bound-resonance transition as the screening parameter increases, we successfully identify the electronic configurations of the numerically obtained resonances. The asymptotic laws for resonance position and width near the critical transition region are extracted, and their connections with the bound-state asymptotic law and Wigner threshold law, respectively, are disclosed. We further find that the birth of a new resonance will distort the trajectories of adjacent higher-lying resonances, while even if two resonances are exactly degenerate in real energy position, they can still be treated as near-isolated resonances provided their widths are significantly different in magnitude.