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Register a new userPartial Times Delay in Elastic Electron Scattering by Rectangular Potential Well with Arising Discrete Levels
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Authors
M. Ya. Amusia
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We have studied the times delay of slow electrons scattered by a spherically symmetric rectangular potential well as functions of the well parameters. We have shown that the electron interaction with the scattering center qualitatively depends on the presence of discrete levels in the well. While electron retention dominates for the potential well with no discrete levels, the appearance of a level leads to the opposite situation where the incident electron hardly enters the scatterer. Such a behavior of the time delay is universal since we found it not only for the first s-level but also for the following arising s-, p-, and d-levels.
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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.
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.
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In two recent papers (Phys. Rev. Lett. {bf 116} (2016) 033201; Phys. Rev. A {bf 94} (2016) 032331), the possibility of continuously varying the degree of entanglement between an elastically scattered electron and the valence electron of an alkali target was discussed. In order to estimate how well such a scheme may work in practice, we present results for elastic electron scattering from lithium in the energy regime of 1$-$5~eV and the full range of scattering angles $0^circ - 180^circ$. The most promising regime for Bell-correlations in this particular collision system are energies between about 1.5 eV and 3.0 eV, in an angular range around $110^circ pm 10^circ$. In addition to the relative exchange asymmetry parameter, we present the differential cross section that is important when estimating the count rate and hence the feasibility of experiments using this system.
Within the framework of a Dirac bubble potential model for the C60 fullerene shell we investigated the angular time delay in slow-electron elastic scattering by C60 as well as average time delay of electrons in this process. It is demonstrated how the angular time delay is connected to the Eisenbud-Wigner-Smith (EWS) time delay. The angular and energy dependences of these times are investigated. The studies conducted shed light to some extent on the specific features of these dependencies.
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