Influence of long-lived metastable levels on the electron-impact single ionization of ${\mathrm{C}}^{2+}$

A joint theoretical and experimental investigation is made of the influence of long-lived metastable levels on the electron-impact single ionization of ${\mathrm{C}}^{2+}$. It is expected that our electron cyclotron resonance ion source produces a beam with 40% of the ${\mathrm{C}}^{2+}$ ions in the $1s^{2}2s^2{}^{1}S_0$ ground level and 60% in the $1s^{2}2s2p{}^{3}P_{0,2}$ excited levels. The comparison of nonperturbative close-coupling calculations with previous single-pass crossed beams and with our multiple-pass storage-ring measurements for the electron-impact ionization of ${\mathrm{C}}^{2+}$ is consistent with the predicted large metastable fraction. Reasonable agreement is found between the present time-dependent close-coupling, $R$-matrix with pseudostates, and converged-close-coupling ionization cross-section calculations for the ground and first excited configuration, and experimental measurement, assuming a 60% metastable fraction in the ion beam. Distorted-wave calculations are found to overestimate the ionization cross section from both the ground and metastable terms, compared with nonperturbative calculations, resulting in an overestimation of the resultant total cross section when compared with experiment. It is clear that collisional-radiative modeling of the evolution of atomic plasmas through the Be-like ionization stage will need to take into account the role of both ground and metastable levels.

Figure 1

Ionization cross sections for the $2s^2$ configuration. The squares show the TDCC results for the $2{\mathrm{s}}^2$ configuration, the dot-dashed line shows the CCC results for the $2s^2{}^{1}S$ term, the dashed line shows the RMPS results for the $2s^2{}^{1}S$ term, and the solid line gives the CADW results for the $2{\mathrm{s}}^2$ configuration. $(1.0\mathrm{Mb}=1.0\times {10}^{-18}{\mathrm{cm}}^2.)$

Figure 2

Ionization cross sections for the $2s2p$ configuration. The open squares show the TDCC results for the direct ionization of the $2s2p$ configuration; the closed squares are the TDCC results with excitation-autoionization included. The dot-dashed line shows the configuration-average CCC results for the $2s2p$ configuration; the dashed line shows the configuration-average RMPS results for the $2s2p$ configuration. The dotted line shows the CADW results for the direct ionization of the $2s2p$ configuration, and the solid line shows the CADW results with excitation-autoionization included. $(1.0\mathrm{Mb}=1.0\times {10}^{-18}{\mathrm{cm}}^2.)$

Figure 3

Theoretical ionization cross sections for ${\mathrm{C}}^{2+}$, assuming 40–60 % mixture of the ground and excited configurations, compared with the experimental results from the CRYRING experiment (diamonds). The theoretical results consist of CCC results (dot-dashed line), TDCC results (open squares for the direct ionization, solid squares for the results with excitation-autoionization), RMPS results (dashed line), and CADW results, including excitation-autoionization (solid line). $(1.0\mathrm{Mb}=1.0\times {10}^{-18}{\mathrm{cm}}^2.)$

Figure 4

Theoretical ionization cross sections for ${\mathrm{C}}^{2+}$, assuming 40–60 % mixture of the ground and excited configurations, compared to the low metastable experimental results from Falk et al. [7] (triangles) and the measurements of Woodruff et al. [10] (open circles). The theoretical results consist of CCC results (dot-dashed line), TDCC results (open squares for the direct ionization, solid squares for the results with excitation-autoionization), RMPS results (dashed line), and CADW results, including excitation-autoionization (solid line). $(1.0\mathrm{Mb}=1.0\times {10}^{-18}{\mathrm{cm}}^2.)$