Electron-impact excitation of forbidden and allowed transitions in Fe ii

Extensive calculations are reported for electron collision strengths, rate coefficients, and transitions probabilities for a wide range of transitions in Fe ii. The collision strengths were calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and a semiempirical fine-tuning procedure is employed for an accurate representation of the target wave functions. The energy correction was also used in the scattering calculations by adding to Hamiltonian matrices prior to transformation to intermediate coupling. The spin-orbit interaction term was added to the final Hamiltonian matrices in scattering calculations. The close-coupling expansion contains 340 fine-structure levels of Fe ii and includes all levels of the $3d^{6}4s$, $3d^{5}4s^2$, $3d^7$, and $3d^{6}4p$ configurations, plus a few lowest levels of the $3d^{5}4s4p$ configuration. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities at electron temperatures in the range from ${10}^2$ to ${10}^5$ K and are reported for all possible inelastic transitions between the 340 fine-structure levels. The present results are more extensive than the previous calculations and considerably expand the existing data sets for Fe ii, allowing a more detailed treatment of the available measured spectra from different space observatories. Comparison with other calculations for collision rates and available experimental radiative rates is used to place uncertainty bounds on our collision strengths and to assess the likely uncertainties in the existing data sets.

Figure 1

Schematic diagram of the lower part of the Fe ii spectrum.

Figure 2

Left panel: Comparison of lifetimes for the first 63 even-parity metastable levels in Fe ii. Red circles, Deb and Hibbert [23]; black squares, Bautista et al. [19]; circles with error bars, experimental data [33, 34, 35, 36]. Right panel: Comparison of the present radiative rates for the forbidden E2 and M1 transitions with the CIV3 calculation by Deb and Hibbert [23].

Figure 3

Upper panel: Collision strengths for the $3d^{6}4s{}^{6}D_{9/2}\text{–}3d^{6}4s{}^{6}D_{7/2}$ (1-2) and $3d^{6}4s{}^{6}D_{9/2}\text{–}3d^7{}^{4}D_{9/2}$ (1-6) fine-structure transitions. Lower panel: Effective collision strength for the (1-2) and (1-6) transitions. Solid curve, present BSR-340 model; dash-dotted curve, the RM-262 calculations of Ramsbottom et al. [17]; dashed curve, the RM-142 calculations of Zhang and Pradhan [9]; solid rectangles, the RM-AV calculations of Bautista et al. [19].

Figure 4

Comparison of effective collision strengths obtained in the present BSR-340 model with the RM-262 [17] (upper panels) and RM-142 [9] (lower panels) for three temperatures. Also indicated in the panels is the average deviation $\sigma$ from the BSR-340 results. Comparison includes the forbidden transitions between the first 52 even-parity levels of Fe ii.

Figure 5

Comparison of effective collision strengths obtained in the present BSR-340 model with the RM-AV results of Bautista et al. [19] at temperature of ${10}^4$ K.

Figure 6

Upper panels: Collision strengths for the $3d^{6}4s{}^{6}D_{9/2}\text{–}3d^{6}4p{}^{6}D_{9/2}^o$ (1-64) and $3d^{6}4s{}^{6}D_{9/2}\text{–}3d^{6}4p{}^{6}F_{11/2}^o$ (1-69) fine-structure transitions. Lower panels: Effective collision strength for the (1-64) and (1-69) transitions. Solid curve, present BSR-340 model; dot-dashed curve, the RM-262 calculations of Ramsbottom et al. [17]; dashed curve, the RM-142 calculations of Zhang and Pradhan [9].

Figure 7

Comparison of effective collision strengths obtained in the present BSR-340 model with RM-262 [17] (left panel) and RM-142 [9] (right panel) for electron temperature $T={10}^4$ K. Also indicated in the panels is the average deviation $\sigma$ from the BSR-340 results. The squares in the left panel represent transitions from the ground level only.