Ionization of atomic hydrogen by electrons: the role of the contributions of the pseudo-states in the second Born approximation

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).

A study of the turn-up effect in the electron momentum spectroscopy

“…From figure 1 we can immediately conclude that the 3C model gives the right amplitude and well describes the ionization process, in contrast to the DWBA and the DWBA-G models. By using a normalization factor of 0.88 for the experiments of Ehrhardt et al [30] we can get a very good agreement between the other set of relative measurements by Lohmann et al [31] and the 3C model [35], exactly like the BBK-EIS and the CCC models.…”

The second Born approximation for the double ionization of N2by electron impact

“…We fix ¯= w 55 eV for all cases, to be not so far from the double ionization energy of N 2 . We remember that Dal Cappello et al [46,49] and Grin et al [48] showed that the second Born approximation when using the closure approximation gives good agreement with experiments if the value of w is close to the value of the single ionization of energy in the case of the single ionization and to the DI of energy for DI. We notice that if we fix w to 65 eV (for instance) we have practically no change.…”

“…w being the average excitation energy. The integration on  q is described in different papers [47][48][49][50][51][52].…”

Theoretical Study of Atomic Excitation by Impact of Protons in the Variational Formalism

“…The value of k has been obtained thanks to the work of Sahlaoui and Bouamoud [8], DalCappello et al [9] and Benmansour et al [10]. Our calculations have therefore been made on an expansion over the finite basis vectors |i and |j consisting of the six states {1s, 2s, 2p 0 , 2p +1 , 2p −1 , kp 0 }.…”