Ellinger Y., Defranceschi M. (eds.) Strategies and applications in quantum chemistry (Kluwer, 200

no experimental data are available, so the most diffuse functions have been optimized with respect to highly accurate atomic data of Chung [32] taking into account relativistic correction terms. The results are reported on Table 2 and show a rather reasonable agreement, the accuracy is of course somewhat poorer than for the ground state

but we are dealing with much more excited states. The comparison with relativistic atomic calculations gives besides an insight over the importance of relativistic terms which seem to be quite negligible with respect to the rate of accuracy reached in such calculations.

The evaluation of the radial coupling matrix elements between molecular states of the same symmetry

has been performed by means of the finite difference technique [33]

For reasons of numerical accuracy, we have performed a three-point differentiation using

electronic coordinates has been generally taken at the N nucleus in order to eliminate the non-vanishing coupling terms at long-range. The importance of possible translation effects

3.Molecular results

3.1.GROUND STATE SYSTEM

curves show no evidence of avoided crossings, but three avoided crossings appear in the

The asymptotic energy values obtained by a configuration interaction calculation at 25 a.u. corrected by the coulombic repulsion term (the 1/R4 term has been neglected) are seen to be in quite good agreement with experiment (Table 3).

The main features of the radial coupling matrix elements are presented in Fig. 2. In correspondence with the avoided crossings between the potential energy curves of singleelectron capture, sharp peaked functions appear at respectively 6.35, 7.50 and 8.30 a.u.. They are approximately 1.23, 2.53 and 12.21 a.u. high and respectively 0.75, 0.50 and less than 0.10 a.u. wide at half height.

4. Collision dynamics

4.1.SINGLE-ELECTRON CAPTURE PROCESS FROM THE GROUND STATE

This is, beyond all doubt, the most important process and the only one which has been already tackled with theoretically. Nevertheless, the prediction given by the classical overbarrier transition model is not correct for this collision [9] and the modified multichannel Landau-Zener model developed by Boudjema et al. [34] cannot explain the experimental results for collision velocities higher than 0.2 a.u.. With regard to the collision energy range, we have thus performed a semi-classical [35] collisional treatment

been neglected in the calculation. The strong radial couplings between the entry channel and the states dissociating to have been fitted by Lorentzian shape functions, while the other couplings and the potential energies have been fitted by spline cubic functions.

The partial cross-sections on the n = 3 levels are displayed in Table 4 and Fig. 6 and show a fairly good overall agreement with the experimental results of Cotte et al. [4,7] and Dijkkamp et al. [9]. From a numerical point of view, the error bar has been estimated

Table 4. Single-electron capture cross-sections on the n = 3 levels

(For comparison with Dijkkamp results, the collision energy is given in parenthesis when different from ours).

344 M.C.BACCHUS-MONTABONNEL

preted by the Landau-Zener model [34]. This feature seems to be driven at high energy by

4.2.SINGLE-ELECTRON CAPTURE PROCESS FROM THE METASTABLE

In consideration with the experimental data available, the collision dynamics has been performed for two energies, 60 and 50 keV, by means of a semi-classical method using the EIKONXS program [36]. As seen in Table 5, the contribution of the levels coupled by rotational couplings appears to be quite negligible over the contribution of the levels for collision energies up to 50 keV. The collisional treatment has thus been performed with

ding besides the transfer-excitation state. The partial cross-sections of capture are presented in Table 6 and compared with the experimental results of Bouchama and Druetta at 60 keV [6]. Taking into account the experimental error bar, which is at least of 30% in view of the weakness of the observed lines, the accordance appears to be quite good. This result gives even confidence in the experimental results which remain particularly difficult to analyse. Besides, the theoretical partial cross-sections are affected by less than 20% by changing the origin of electronic coordinates, which is far behind the experimental error bar.

Table 5. Values of the single-electron capture cross-sections for the states

A comparison of the partial cross-sections of capture at 50 keV, for the collision with He

metastable. This shows, a posteriori, that neglecting the fraction of metastable — which is often done when no informations are available — should not lead to too high an experimental error bar.