The classical limit of ionization in fast ion-atom collisions

Abstract

The authors study the classical-quantum correspondence for ionization in three-body fast ion-atom collisions. The existence of a classical limit of the quantum mechanical transition probabilities as a function of the momentum transferred to the electron during the collision, the impact parameter, the energy and angle of the emitted electron, and the initial quantum level of the target is investigated. A well behaved classical limit is shown to exist for large momentum transfers whereas ionization by small momentum transfers or at large impact parameters is shown to be classically suppressed. It is found that ionization at small impact parameters does not possess a well-defined classical limit. Modifications of classical trajectory Monte Carlo (CTMC) methods to account for non-classical ionization are suggested. Applications related to recent data for electron ejection into large angles are presented.

Total cross sections for ionizing processes induced by proton impact on molecules of biological interest: A classical trajectory Monte Carlo approach

“…Whereas our theoretical results exhibit a very good agreement with the recent calculations of Errea et al for describing the CI process [13], we clearly observe an underestimation of the results reported by Gervais et al in [14] (see Panel c)) for the DI process. This large disagreement is actually not well understood but highlights the limitation of the CTMC approach to treat the DI process as already mentioned by Reinhold and Burgdörfer [26] who have shown that in the IEM approximation, the double ionization was badly described by classical models. Finally, note that some of the SI and DI results reported in Panels a) and c) have been calculated for liquid water [14] whereas our results concern water vapor.…”

Energy and angular distributions of electrons from ion impact on atomic and molecular hydrogen. II. 20–114-keVH++H

“…In contrast to the perturbation methods, this approach is most applicable when the projectile ion-electron interaction is strong. When this occurs, a very large number of quantum states become populated and their superposition may be successfully mimicked quasi-classically [17]. For weak perturbations, this approach breaks down, as will become clear through the comparisons with experiment and the other theories presented here.…”

“…At intermediate impact velocities this translates into a sizable classical underestimation of the cross sections for emission of electrons into very large, backward, angles. To overcome these classical deficiencies, we present here results of a combined model in which the quantummechanical (B1) results for small momentum transfers are added to the CTMC cross sections [17], which we denote CTMC-I-B1. In this model, we compute the Born approximation limited to momentum transfers Ap, smaller than a critical value given by where Z , is the target nuclear charge and n is the initial electronic principal quantum number, as described in Ref.…”

“…In this model, we compute the Born approximation limited to momentum transfers Ap, smaller than a critical value given by where Z , is the target nuclear charge and n is the initial electronic principal quantum number, as described in Ref. [17]. In this case, since Z , = 1 and n = 1, Apc =2/3/8.…”

Impact-parameter dependence of the electronic energy loss of fast cluster projectiles

“…(1)) that are valid for a limited range of impact parameters and in a second step these approximations should be linked. At large impact parameters the dipole approximation for V i can be used, and thus, an analytical expression [19,20] for Q (b) may be obtained. Inserting the cluster interacting potential, we have, for large impact parameters, an expression of the form…”