A method of calculating the cross sections of inelastic vibronic transitions in collisions of slow electrons with polyatomic molecules in the framework of the local theory (the 'boomerang' model) is proposed. The method is based on the study of the time evolution of the initial vibronic wavefunction; the evolution is governed by the (complex valued) Hamiltonian of the intermediate anion state. The method has been applied to the consideration of inelastic electron collisions with the CO2 molecule in the two-mode approximation (symmetrical stretching and bending). The results obtained demonstrate the importance of the two-mode description for the system which can undergo the Renner transition.
The processes with two electrons in the final continuum state are considered for small energy excess E above the threshold. The distribution of the total energy E between the electrons is calculated within the quantum Wannier theory where the quadratic approximation for the Hamiltonian is employed in the vicinity of the Wannier ridge. The problem is cast in terms of the wavepacket propagation. The Green function formulation is employed and its physical implications are analysed. The final distribution is shown to be uniform and essentially independent of the boundary condition at the border of the inner Wannier zone. The extended model is developed which does not resort to the quadratic approximation but accounts for the attractive Coulomb singularities of the potential. It is solved numerically using the grid method. The manifestations of the competing process are discussed (single ionization with the other electron in a high Rydberg state).
Abstract. The Wannier [13 theory describes the escape of two electrons from a charged core in the threshold domain. Its modification [3] is applied to some features of the double escape processes which were not analyzed previously in due extent. The behaviour of the total cross sections for a small, but finite, energy excess E above the threshold is described incorporating the deviations from the well known Wannier power law. The processes with the escape of electron and positron from the core are also considered. The energy dependence of the spin asymmetry A in (e, 2e) collisions is analyzed in connection with the recent experimental data (which seem to manifest some dependence A(E) in the near-threshold domain contrary to the conventional Wannier theory). The theory suggests the requirements for the accuracy of the experiments intended to verify the Wannier threshold laws and detect the deviations from them.
The method of an accurate calculation of vibrational excitation cross sections of a two-mode molecule by slow electrons within the framework of the local theory (the 'boomerang' model) is applied for a model study of the excitation of the symmetrical stretching vibrational modes of carbon dioxide in the two-mode approximation (i.e., only the symmetrical stretch and bending modes are included in the consideration). It is shown that the 'boomerang' oscillations in the cross section are strongly suppressed due to the decay of the one-dimensional 'boomerang' state caused by the anion wave packet sliding from the linear configuration ridge. Consequently, the bending motion in CO molecule should to be taken into account even if only the processes without the final bending excitation are considered. A simple quasi one-dimensional model describing the system sliding from the ridge is put forward which treats this phenomenon as a decay of the initial wave packet via the series of diabatic resonant states related to unstable trajectory.
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