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

TL;DR

This paper studies how the Wigner time delay in slow elastic electron scattering by a spherical potential well changes as the well's parameters vary, especially when discrete bound states emerge, revealing sign changes and jumps in delay.

Contribution

It extends previous one-level analysis to multiple bound states, showing how the emergence of s-levels causes sign changes and jumps in the Wigner time delay.

Findings

Time delay is positive without bound states, turns negative after levels appear.

Significant jumps in time delay occur at the emergence of each new bound state.

Time delay sign changes also occur when varying the well radius R.

Abstract

We generalize here the one-level consideration in our recent paper arXiv:1901.00411 [1] to the case when an electron collides with a potential that have any number of s bound states. We investigate peculiarities in the Wigner time delay behavior for slow electron elastic s-scattering by spherically symmetric square-potential well. We have considered potential wells, the variation of parameters of which (potential depth U and its radius R) lead to arising arbitrary number of s bound states. We demonstrate that while the time delay for potential wells with no discrete s-levels always has a positive value for small electron energies, it changes sign after level arising. We found that at the moments of arising in the well not only of the first but also following s-levels as well, the time delay as a function of U experiences instant jumps from a positive value to a negative one. The amplitudes of these jumps increases with decrease of the electron wave vector k. The times delay for potential well, the variation of the radius of which R leads to the appearance of discrete levels, also change sign at these critical radii.