Electron-ion recombination of $\mathrm{Si}\mathrm{IV}$ forming $\mathrm{Si}\mathrm{III}$: Storage-ring measurement and multiconfiguration Dirac-Fock calculations

The electron-ion recombination rate coefficient for $\mathrm{Si}\mathrm{IV}$ forming $\mathrm{Si}\mathrm{III}$ was measured at the heavy-ion storage-ring TSR. The experimental electron-ion collision energy range of $0$–$186\mathrm{eV}$ encompassed the $2p^{6}nl{n}^{\prime }{l}^{\prime }$ dielectronic recombination (DR) resonances associated with $3s\to nl$ core excitations, $2s2p^{6}3snl{n}^{\prime }{l}^{\prime }$ resonances associated with $2s\to nl$ $(n=3,4)$ core excitations, and $2p^{5}3snl{n}^{\prime }{l}^{\prime }$ resonances associated with $2p\to nl$ $(n=3,\dots ,\infty )$ core excitations. The experimental DR results are compared with theoretical calculations using the multiconfiguration Dirac-Fock (MCDF) method for DR via the $3s\to 3p{n}^{\prime }{l}^{\prime }$ and $3s\to 3d{n}^{\prime }{l}^{\prime }$(both $n^{\prime }=3,\dots ,6$) and $2p^{5}3s3l{n}^{\prime }{l}^{\prime }$ $(n^{\prime }=3,4)$ capture channels. Finally, the experimental and theoretical plasma DR rate coefficients for $\mathrm{Si}\mathrm{IV}$ forming $\mathrm{Si}\mathrm{III}$ are derived and compared with previously available results.

Figure 1

Measured $\mathrm{Si}\mathrm{IV}$ to $\mathrm{Si}\mathrm{III}$ merged-beams electron-ion recombination rate coefficient in the energy range dominated by DR resonances associated with $3s\to 3p$ core excitations. The vertical bars below the spectrum denote the $2p^{6}3p{n}^{\prime }{l}^{\prime }$ DR resonance positions as expected on the basis of the hydrogenic Rydberg formula [Eq. (8)]. Note that resonances up to $n=15$ are individually resolved. The vertical arrows around $3\mathrm{eV}$ denote the positions of the $2p^{6}3d^2{}^{3}F$ and $2p^{6}3d^2{}^{1}G$ doubly excited states. The inset shows the recombination rate coefficient at energies below $2\mathrm{eV}$, where it is dominated by $2p^{6}3p4l^{\prime }$ resonances.

Figure 2

Measured $\mathrm{Si}\mathrm{IV}$ to $\mathrm{Si}\mathrm{III}$ merged-beams electron-ion recombination rate coefficient in the energy range of DR resonances associated with $3s\to 3d$ core excitations. The vertical bars denote the $2p^{6}3d{n}^{\prime }{l}^{\prime }$ DR resonance positions as expected on the basis of the hydrogenic Rydberg formula [Eq. (8)]. The error bars on each data point show the statistical uncertainties.

Figure 3

Measured $\mathrm{Si}\mathrm{IV}$ to $\mathrm{Si}\mathrm{III}$ merged-beams recombination rate coefficient in the electron-ion collision-energy region of resonances associated with $\mathrm{\Delta }N\ge 1$ $2s\to nl$ and $2p\to nl$ $(n\ge 3)$ inner shell core excitations.

Figure 4

Measured $\mathrm{Si}\mathrm{IV}$ to $\mathrm{Si}\mathrm{III}$ merged-beams rate coefficient at energies below $1.5\mathrm{eV}$ (circles and gray shaded area). The solid curve is the sum of a fit comprising 25 fitted DR resonances (dashed curves cf. Sec. 5A) and the nonresonant rate coefficient due to RR (dotted curve). The inset shows the same curves, but in more detail in the energy range $1$–$100\mathrm{meV}$.

Figure 5

Comparison of the experimental $\mathrm{Si}\mathrm{IV}$ DR spectrum (open circles) in the energy region $0-1.5\mathrm{eV}$ with various theoretical results (solid curves). Figures (a), (b), and (c) show our multiconfiguration Dirac-Fock (MCDF) method results and (d) published relativistic many-body perturbation theory (RMBPT) calculations (Ref. 12). The nonresonant part of the recombination rate coefficient due to radiative recombination (RR) was subtracted from the measured curve (see text). In the MCDF calculation three different approximations have been applied to the enlarged CSF basis including all the fine-structure states from the $nl{n}^{\prime }{l}^{\prime }$ $(n,n^{\prime }=3,4,5,6)$ configurations: (a) Using the orbital functions from the doubly excited $3l{n}^{\prime }{l}^{\prime }{}^{2S+1}L_J$ levels for the representation of both the initial and final states; (b) with an independent optimization of the sodium- and magnesiumlike states but without including the exchange interaction between the initially free electron and the bound-state electrons; (c) the same as in (b) but by incorporating the exchange interaction with regard to the bound-state density.

Figure 6

Comparison of the experimental $\mathrm{Si}\mathrm{IV}$ DR spectrum (open circles) in the energy region $0-6\mathrm{eV}$ with the final result of the MCDF calculation (solid line). This energy range includes $2p^{6}3p{n}^{\prime }{l}^{\prime }$ $(4\le n^{\prime }\le 6)$ and $2p^{6}3d^2$ resonances. The nonresonant part of the recombination rate coefficient due to RR was subtracted from the measured curve (see text).

Figure 7

Comparison of experimental $\mathrm{Si}\mathrm{IV}$ DR spectrum (open circles) in the energy region of the $2p^{5}3s3l{n}^{\prime }{l}^{\prime }$ resonances with the results of our MCDF calculation (solid line). The nonresonant part of the recombination rate coefficient due to RR was subtracted from the measured curve (see text).

Figure 8

Comparison between the experimental merged-beams DR rate coefficient (open circles with solid line) and the AUTOSTRUCTURE calculation. The AUTOSTRUCTURE calculation was multiplied by a factor of 1.13 (see text). The dashed line is the theoretical result with account for the experimental field ionization of high-$n$ Rydberg states using the field ionization model of Ref. [6]. The shaded area highlights the unmeasured purely calculated part of the composite DR rate coefficient.

Figure 9

Experimentally derived $\mathrm{Si}\mathrm{IV}$ to $\mathrm{Si}\mathrm{III}$ DR rate coefficient in a plasma (thick solid line) comprising $\mathrm{\Delta }N=0$ DR (Figs. 1, 2), $\mathrm{\Delta }N=1$ and 2 DR (Fig. 3), and the theoretical estimate for the unmeasured contributions of states with $n\ge 17$ for $\mathrm{\Delta }N=0$ DR (Fig. 8). The error bars denote the $\pm 18\%$ $\left(1\sigma \right)$ experimental uncertainty in the absolute rate coefficient. The experimental results without DR extrapolation is shown by the thin solid line. Also shown are recent theoretical calculations of the DR rate coefficient by Gu [46] (thick dash-dot-dotted line, labeled Gu) and Altun et al. [37] (thick dash-dotted line, labeled Altun), and the recent experimental DR rate coefficient by Orban et al. [9] (thick dashed line, labeled Orban). The contribution from the experimentally measured DR resonances between 0 and $6\mathrm{eV}$ is shown as the thin dotted line (labeled Exp $<6\mathrm{eV}$) while the contribution of the MCDF calculation in the same energy range is shown as thick dotted line (labeled MCDF). A recent calculation of the plasma RR by Badnell [47] is shown as the thin dash-dot-dotted line labeled RR Badnell. The temperature ranges where $\mathrm{Si}\mathrm{IV}$ is expected to peak in abundance in photoionized plasmas (labeled PP) and collisionally ionized plasmas (labeled CP) are highlighted.