Behavior of Regge Poles with Increasing Potential Strength

We illustrate, using the example of a model but realistic potential, that the family of the Regge pole trajectories (RPT) moves to the right along the real l-axis with increasing atomic charge Z. Every time Z exceeds Z=Z$_{N}$, the Z at which the Nth bound s-state first appears at zero energy, one more trajectory joins the RPT family in the first quadrant of the complex l-plane, coming from the left side of the real l-axis. Since for atoms with Z$<$ Z$_{N }$a part of the RPT rise off the real l-axis near but before integer values of l we can expect that for such atoms there will be resonances in electron scattering cross sections . The number of resonances depends on N=n+l (n is the principal quantum number)$^{1}$. We have calculated energies and widths for these resonances in the model potential using a perturbation theory approach.