Theoretical Confirmation of the Low Experimental $3C/3D$ $f$-Value Ratio in Fe xvii

Radiative transition probabilities ($A$ values) are computed for the Fe xvii $L$-shell lines in a Breit-Pauli configuration-interaction method with the autostructure atomic structure code. It is shown that, by carefully taking into account the fine-tuning of the relativistic coupling and $2p$-orbital relaxation, the measured $A$ values of the $M1$ and $M2$ lines and, for the first time, the low $f(3C)/f(3D)$ oscillator-strength ratio are satisfactorily reproduced by the theory. The present ratio $f(3C)/f(3D)=2.82$ compares well with the measurement of $2.61\pm 0.23$ by x-ray laser spectroscopy.

Figure 1

Fe xvii energy-level diagram (not drawn to scale) showing the spectral lines of interest.

Figure 2

$\mathrm{\Delta }E({\overline{\overline{2p}}}^{5}3d{{}^{3}D}_1^o,{\overline{\overline{2p}}}^{5}3d{{}^{1}P}_1^o)$ energy difference (top panel) and $f(3C)/f(3D)$ ratio (bottom panel) as a function of the $\lambda (\overline{\overline{2p}})$ scaling parameter. The spectroscopic value of $\mathrm{\Delta }E=13.36\mathrm{eV}$ is never reached, but the procedure allows an optimized value of $\lambda (\overline{\overline{2p}})=1.24$ to be determined. $f(3C)/f(3D)$ are obtained after the TECs are applied, resulting in a value of 2.82 with the optimized scaling parameter.