Absolute rate coefficients for photorecombination and electron-impact ionization of magnesiumlike iron ions from measurements at a heavy-ion storage ring

Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of ${\mathrm{Fe}}^{14+}$, forming ${\mathrm{Fe}}^{13+}$ and ${\mathrm{Fe}}^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of ${\mathrm{Fe}}^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where ${\mathrm{Fe}}^{14+}$ is expected to form in such plasmas, the latest theoretical rate coefficients of Altun et al. [Astron. Astrophys. 474, 1051 (2007)] for PR and of Dere [Astron. Astrophys. 466, 771 (2007)] for EII agree with the experimental results to within the experimental uncertainties. Common features in the PR and EII resonance structures are identified and discussed.

Figure 1

Calculated time-dependent fractional populations of the ${}^{57}$${\mathrm{Fe}}^{14+}$$\left(3s^2{}^1{S}_0\right)$ ground level (thick solid line) and of the excited levels $3s3p{}^3{P}_0$, ${}^3{P}_1$, ${}^3{P}_2$, and ${}^1{P}_1$ (dashed line, dotted line, dash-dotted line, and dash-dot-dotted line, respectively). The thin solid line is the sum of the populations of the 136 higher excited levels that were also considered in the calculation. The shaded area marks the time interval that was typically used for taking data.

Figure 2

Measured merged-beams rate coefficient for PR of ${\mathrm{Fe}}^{14+}$ in the energy ranges of the (a) $3\to 4$ $\Delta N=1$ DR resonances [Eq. (1)] and (b) $2\to 3$ $\Delta N=1$ DR resonances [Eqs. (1) and (1)]. The vertical bars denote calculated resonance positions [Eq. (3)]. Numbers at the leftmost vertical bars denote the value of the lowest Rydberg principal quantum number $n$ considered. Some of the resonances in panel (a) may be associated with $\Delta N=0$ DR $3s\to 3d$ core excitations. The dashed white line in panel (a) is the theoretical rate coefficient for RR of ${\mathrm{Fe}}^{14+}$, calculated by using a semiclassical hydrogenic formula with field-ionization cutoff beyond $n_{\max }=53$ [30]. The RR rate coefficient has not been plotted in panel (b), where it is practically zero on the displayed rate-coefficient scale.

Figure 3

Rate coefficients for DR of ${\mathrm{Fe}}^{14+}$$\left(3s^2{}^1{S}_0\right)$ ions in a plasma. The thick full line is our present experimentally derived rate coefficient. The error bars denote its $\pm 26\%$ uncertainty. Our previous result [11] that only comprised $\Delta N=0$ DR [Eq. (1)] is shown as a thin full line. The present additional contributions by $3\to 4$ $\Delta N=1$ DR [Eq. (1)] and by $2\to 3$ $\Delta N=1$ DR [Eqs. (1) and (1)] are shown as dashed and dash-dotted curves, respectively. The thin dotted curve is the recommended rate coefficient from Arnaud and Raymond [47]. The most recent theoretical result of Altun et al. [12] is shown as a (red) short-dashed line. The temperature ranges where ${\mathrm{Fe}}^{14+}$ is expected to form in photoionized plasmas (PP) [48] and collisionally ionized plasmas (CP) [49] are indicated as gray shaded areas.

Figure 4

Cross sections for EII of ${\mathrm{Fe}}^{14+}$ forming ${\mathrm{Fe}}^{15+}$. The electron-ion collision energy scale is logarithmic. The thin (black) solid line is the present experimental result. The capped error bars represent the $\pm 26\%$ systematic experimental uncertainty. The dotted (magenta) line is the theoretical result of Dere [13]. The thick (red) solid line is the theoretical result of Mitnik et al. [24]. Their theoretical DI cross section is shown separately as a (red) dashed line. Vertical arrows mark DI ionization thresholds. Energy ranges [24] for the various $2p\to n^{\prime }{l}^{\prime }$ EA thresholds [Eq. (2)] are also indicated. The inset enlarges the energy range around the threshold for DI of a $3s$ valence electron. The threshold energies in the inset were taken from [51].

Figure 5

Rate coefficients for EII of ${\mathrm{Fe}}^{14+}$ in a plasma. The thin and thick solid lines are the present experimentally derived rate coefficients excluding and including the extrapolation by theory, respectively. The error bars correspond to the $\pm 26\%$ systematic experimental uncertainty. The short-dashed (red) line is the recommended rate coefficient of Dere [13], the short-dash-dotted (blue) line is the rate coefficient of Mitnik et al. [24], and the dotted curve is the recommended rate coefficient of Arnaud and Raymond [47]. The temperature range where ${\mathrm{Fe}}^{14+}$ is expected to form in a collisionally ionized plasma (CP) is indicated as a gray shaded area. It is the same temperature range as in Fig. 3.

Figure 6

Cross sections for recombination and ionization of ${\mathrm{Fe}}^{14+}$ forming ${\mathrm{Fe}}^{13+}$ (a) and ${\mathrm{Fe}}^{15+}$ (b) in the collision energy range of ionization resonances. Panel (c) provides a magnified view of the ionization resonances, which has been created by subtraction of the arbitrarily drawn smooth white dashed line in panel (b) from the measured ionization cross section. The vertical dashed lines mark corresponding resonances in the DR and EII spectra.