Deep interference minima in experimental ionization differential cross sections

Fundamental to the understanding of all physical processes on an atomic scale is a theoretical framework based upon quantum mechanics and wave-particle duality. The success of the quantum theory has been proven time and again, and has led to many of the technological and scientific advances that evolved during the latter part of the 20th century. This theory provides the framework for all successful models of atomic, molecular, and nuclear reactions including elastic scattering, excitation, ionization, and fragmentation. Under certain conditions the wave nature of the particles manifests itself directly, allowing characteristics of this nature to be measured. The most usual manifestations are diffraction and interference, where both the amplitude and phase of the wave front play a key role. Diffraction of electrons at a boundary is routinely observed in electron microscopy, and can be directly related to the de Broglie wavelength determined from the electron momentum. Wave effects such as interference minima are less frequently observed, since a coherent summation of both the amplitudes and phases of contributing wave vectors relating to the process under study is necessary to produce a minimum. One striking example where quantum-mechanical interference is seen is in elastic scattering of electrons from atoms @1–3#. In this case, a number of minima are observed in the elastic differential cross section as a function of scattering angle. This is a direct result of the complex scattering amplitudes relating to the incident and scattered electrons adding coherently to produce minima in the cross section. A further manifestation of interference is seen in electronimpact ionization through a resonance target state. In this case, a Fano profile may be observed in the scattered electron cross section @4,5#. This is a result of an interference between two possible pathways to the continuum, either directly or via the resonance state. Observations of strong interference effects in electronimpact experiments become fewer as the complexity of the reaction increases, since the probability of occurrence of these minima decreases. This is a consequence of the stringent requirement that both the amplitude and phase of the scattering amplitudes contributing to the reaction must coherently add to be very small to produce a sharp minimum in the measured cross section. For inelastic electron-scattering experiments involving target excitation, the incident channel involves an electron and a neutral target, as does the final channel following excitation. It is necessary to include the complex process of resonant target excitation in the model,