Special features of Wigner times delay in slow elastic electron scattering by shallow potential well

TL;DR

This paper studies how Wigner time delay behaves in slow elastic electron scattering by shallow potential wells, revealing sign changes and jumps associated with bound state formation and dependence on well parameters.

Contribution

It presents a detailed analysis of Wigner time delay features in shallow potential wells, highlighting the impact of bound state emergence on delay behavior.

Findings

Time delay is positive for no bound states and changes sign after bound state formation.

A jump in time delay occurs at the moment of bound state emergence.

Time delay depends strongly on the geometrical sizes of the potential wells.

Abstract

We investigate specific features in the Wigner time behavior for slow electron elastic scattering by shallow potential wells. We considered two types of potentials wells, the small changes in the parameters of which lead to arising bound states in the well. It appeared that the time delay for attractive potential wells with no bound levels always has a positive value for small electron energies and changes sign after level arising in the well. At the moment of arising the times delay has a jump. The value of this jump is as more as less is the difference in the potential well depth from its critical value. The values of times delay strongly depend on geometrical sizes of potential wells.