Dielectronic recombination of Er-like tungsten

Theoretical studies of dielectronic recombination, a very important process for both atomic and plasma physics, are carried out for low-ionized Er-like W. The dielectronic recombination (DR) of the Er-like ion W${}^{6+}$ proceeds via electron capture into the intermediate autoionizing states of the Tm-like ion W${}^{5+}$ followed by the radiative decay to singly-excited bound states. In particular, energy levels, radiative transition probabilities, and autoionization rates for [Cd]$4f^{14}5p^{5}5l^{\prime }nl$, [Cd]$4f^{14}5p^{5}6l^{\prime \prime }nl$, [Cd]$4f^{13}5p^{6}5l^{\prime }nl$, and [Cd]$4f^{13}5p^{6}6l^{\prime \prime }nl$ ($l^{\prime }=d,f,g$, $l^{\prime \prime }=s,p,d,f,g$, $n=5–7$) states in Tm-like tungsten (W${}^{5+}$) are calculated using the relativistic many-body perturbation theory and relativistic all-order single-double method as well as the Hartree-Fock-relativistic method (cowan code). Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines. DR rate coefficients are determined for the singly-excited [Cd]$4f^{14}5p^{6}nl$ ($n=5–7$) and nonautoionizing doubly-excited [Cd]$4f^{14}5p^{5}5d^2$, [Cd]$4f^{13}5p^{6}5d^2$, [Cd]$4f^{13}5p^{6}6s^2$, [Cd]$4f^{13}5p^{6}5d6s$, and [Cd]$4f^{13}5p^{6}5d6p$ states. Also, contributions from the autoionizing doubly-excited [Cd]$4f^{14}5p^{5}5l^{\prime }nl$, [Cd]$4f^{14}5p^{5}6l^{\prime \prime }nl$, [Cd]$4f^{13}5p^{6}5l^{\prime }nl$, and [Cd]$4f^{13}5p^{6}6l^{\prime \prime }nl$ states (with $n$ up to 100), which are very important for calculating total DR rates, are estimated. Synthetic dielectronic satellite spectra from Tm-like W are simulated in a broad spectral range from 140 to 1200 Å. These relativistic calculations provide recommended values critically evaluated for their accuracy for a number of W${}^{5+}$ ion properties useful for a variety of applications, including for fusion applications.

Figure 1

Synthetic spectra of dielectronic satellite lines for transitions between the $4f^{14}5p^{5}5l^{\prime }nl+4f^{14}5p^{5}6l^{\prime \prime }nl+4f^{13}5p^{6}5l^{\prime }nl+4f^{13}5p^{6}6l^{\prime \prime }nl$ ($l^{\prime }=d,f$, $l^{\prime \prime }=s,p,d,f$, $n=5–7$) autoionizing states and the $4f^{14}5p^{6}nl$ single-excited states of Tm-like tungsten at $T_e=20$ eV. Resolution power, $R=\lambda /\Delta \lambda =500$ (top left and bottom left panels), 3000 (top right panel), and 400 (bottom right panel), is assumed to produce a Gaussian profile. The scale in the ordinate is in units of 10${}^{-15}$ cm${}^3/$s.

Figure 2

Contributions of the $4f^{14}5p^{5}5l^{\prime }nl$ ($n=5–7$), $4f^{13}5p^{6}5l^{\prime }nl$ ($n=5–7$), $4f^{14}5p^{5}6l^{\prime }nl$ ($n=6–7$), and $4f^{13}5p^{6}6l^{\prime }nl$ ($n=6–7$) configurations to the DR rate coefficients ${\alpha }_d(4f^{14}5p^6,j)$ for $j=4f^{14}5p^{6}nl{}^{2}L$ states in Tm-like tungsten as a function of $T_e$. Curve 5 represents the data calculated using scaling formula for $n$ from 8 to 100 (see text for more details).

Figure 3

DR rate coefficients ${\alpha }_d(4f^{14}5p^6,j)$ for the $j=4f^{14}5p^{6}ns{}^{2}S$, $4f^{14}5p^{6}np{}^{2}P$, $4f^{14}5p^{6}nd{}^{2}D$, $4f^{14}5p^{6}nf{}^{2}F$, and $4f^{14}5p^{6}ng{}^{2}G$ levels in Tm-like tungsten as a function of $T_e$.

Figure 4

Sum of the contributions from the doubly-excited nonautoionizing $4f^{14}5p^{5}6s^2$, $4f^{14}5p^{5}5d^2$, $4f^{14}5p^{5}5d6s$, $4f^{14}5p^{5}5d6p$, $4f^{13}5p^{6}6s^2$, $4f^{13}5p^{5}5d^2$, $4f^{13}5p^{6}5d6s$, and $4f^{13}5p^{6}5d6p$ configurations of Tm-like tungsten to the total DR rate coefficients ${\alpha }_d\left(4f^{14}5p^6\right)$ of Er-like tungsten as function of $T_e$.

Figure 5

Sum of the contributions from the singly-excited $4f^{14}5p^{6}nl$ states of Tm-like tungsten to the total DR rate coefficients ${\alpha }_d\left(4f^{14}5p^6\right)$ of Er-like tungsten as function of $T_e$.

Figure 6

Contributions from the singly-excited ${\alpha }_d^{\mathrm{sing}}\left(4f^{14}5p^6\right)$ and doubly-excited nonautoionizing ${\alpha }_d^{\mathrm{doub}}\left(4f^{14}5p^6\right)$ states to the total DR rate coefficients ${\alpha }_d\left(4f^{14}5p^6\right)$ in Er-like tungsten as function of $T_e$. Curve 3 shows the combined scaled contributions illustrated by curve 2 of Fig. 4 and curves 2 and 3 of Fig. 5.