**Figure 13.** Same as figure 1, but the results of the first Born approximation are represented by a dotted line, those of the second Born approximation calculated by using the closure approximation: \bar w = 0 au by a dashed line, \bar w = 0.5 au by a full curve, \bar w = 2.5 au by a dash–dotted line and experiments by squares.

**Abstract**

The second Born approximation is often used, particularly when we study double processes such as the ionization–excitation and the double ionization of atoms and molecules by charged particles. But when we apply this approximation, it needs the knowledge of all excited states of the target. In this study, we apply the second Born approximation by using 294 excited and pseudo-states for the ionization of atomic hydrogen by electrons. We compare the results of our model with those given by other models and to all experiments performed with an incident energy of 250 eV. We show that our new version of the second Born approximation gives better agreement than previous versions even for high values of the energy of the ejected electrons (50 eV).