Example: electron-impact excitation of dipole-forbidden transitions in atoms

Dipole-forbidden transition is defined as transition with zero matrix element of dipole operator. This kind of transition weakly interacts with radiation in visible and near-lying spectral range but may be effectively excited by electron impact. Cross section of this process can be calculated in the frame of Born-Ochkur approximation. The atomic wave functions are determined in the same way as in the case of inter-combined transitions. The comparison of Born-Ochkur results with experimental data and other theoretical treatments is shown in the following figures:

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