Interference resonance/potential scattering

While we have developed the theory of wave-packet scattering and resonances in the context of potential scattering of electrons it is easy to generalise. In particular there is no reason why the scattered particle should not be a photon. In this case the wave packet does not spread and the formalism is valid for general values of 3. Wave packets are known whose widths correspond to a lifetime of order lO s, which is easily resolved with nanosecond electronics. Such wave packets arise in the photon decay of many atomic states. The time spectrum of detected photons is given by (r,t)p for X < 0. We see from (4.166) that this involves an interference between a term whose lifetime is h/3 and one whose lifetime is Xr. The resulting time oscillations have been observed experimentally. They are called quantum beats. 

An exception occurs at high neutron energy, where the cross section for interference between resonant and potential scattering must be included (see Section VIII and Appendix C). 

At the high energies, the total cross section in the denominator of the integrals in (54) must also include the cross section for interference between resonance and potential scattering ... 

The functions (10.188), (10.191), and (10.192) may be used to obtain the generalization of the effective resonance integral in both the NR and NRIA approximations to the case of Doppler broadening. The calculation which follows is developed from the resonance-integral formulas for the homogeneous system and does not include the interference between resonance and potential scattering thus, we take b == 0. This result will be a good approximation for two situations of practical... 

In this section the electron-scattering transition probability amplitude through an open QD, t( ), has been studied for a real-space 2D model Hamiltonian. A sharp change of the phase of t E) by tt occurs when t E) intersects the origin. It implies that two conditions should be satisfied in order to observe a sharp drop of the phase by tt in the tail of the resonant peak. One condition is t Eo) = 0, whereas the second condition is dt E)/dE EQ 7 0. We have shown that this phase drop is a resonance interference phenomenon that happens even within the framework of an one electron effective QD potential. The fact that the QD has at least 2D is a crucial point in the mechanism we have presented here. Our explanation of a sharp phase change is based on the destructive interference between neighboring resonances and thus differs from the mechanism based on the Fano resonance (see, for example. Refs [22,25]). 

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