Time delay in slow electron elastic scattering by potentials with arising levels

We study Wigner time delay of slow electrons by spherically symmetric square potential well as a function of the well parameters. We show that the electron interaction with scattering center qualitatively depends on presence of discrete levels in the well. Electron retention mode by a potential well with no discrete level is replaced by the mode at which after level appears the incident electron hardly enters the scatterer. This behavior of time delay is universal since it is typical not only for the first but also for following arising s-levels.