Peculiarities of Wigner time delay in slow-electron elastic scattering by a potential well with arising discrete levels

We have investigated here the specific features in the Wigner time delay behavior for slow-electron elastic $s$-scattering by spherically symmetric square-potential wells. We have considered the potential wells, the small changes in the parameters of which lead to arising of bound states in the wells. It has been shown that the time delay for shallow potential well with no bound levels always has a positive value for small electron energies and changes its sign after level arising. It has been found that at the moments of the arising of the first and next $s$-levels in the well, the time delay of slow electrons scattered by potential well experiences instant jumps from a positive value to a negative one. The amplitudes of these jumps are the bigger, the smaller is the electron momentum $k$.