The main interest is in the fine-structure transitions 2s²2p^{4 3}P_J →2s²2p^{4 3}P_J' . A symmetrized close-coupled semi-classical method is used, with the proton following hyperbolic trajectories, as described by Alder and Winther [1] and Ryans et al [2].
Several approximations for the radial factor of the interaction matrix elements are tested. The scaled-hydrogenic approximation [2], has the virtue of giving analytic expressions. More accurate HF radial orbitals were also considered. The changes to the cross sections are slight.
The effect of allowing, via a polarization potential, for dipole-coupling between the ground 2s²2p⁴ configuration and the 2s2p⁵, 2s²2p³3s, 2s²2p³3d configurations has been examined. This dramatically reduces the excitation cross sections. The main contribution to the polarization potential is from the 2s2p⁵ state, the more so as Z increases.
As noted by Landman [3], there is significant singlet-triplet mixing within the 2s²2p⁴ states for ions with higher Z. The introduction of this singlet-triplet mixing causes appreciable changes to the cross sections for ions Ca¹²⁺ and heavier. We also obtained the cross sections for the transitions ³P →¹D, ¹S.
To allow for finite densities, we have included plasma screening effects using the Debye-Hückel model as described by Zygelman and Dalgarno [4]. For the electric-quadrupole transitions considered here, plasma screening only becomes significant for small Debye lengths: for Fe¹⁸⁺ the screening cuts in for Λ < 10a₀. This is consistent with work by other authors on hydrogenic ions [4,5].

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