Transition energies and oscillator strengths for the intrashell and intershell transitions of the C-like ions in a thermodynamic equilibrium plasma environment

We present a theoretical study of the transition energies $\omega$ and the oscillator strengths $gf$ for the C-like ions (with $Z$ from 14–36) subject to plasma environment for atomic transitions, which meet the spatial and temporal criteria of the Debye-Hückel (DH) approximation. Two strong dipole-allowed transitions, viz., the intrashell transition $2s2p^3{}^3{D}_1\to 2s^{2}2p^2{}^3{P}_0$, and the intershell transition $2s^{2}2p3d{}^3{D}_1\to 2s^{2}2p^2{}^3{P}_0$ are investigated in detail. We found that both $\omega$ and $gf$ increase for the intrashell transition under the Debye-Hückel screening potential $V_{DH}$ in terms of the Debye length $D$, which is linked to the ratio between the plasma density $N_e$ and its temperature $kT$. In contrast, both $\omega$ and $gf$ decrease for the intershell transition. Our theoretically estimated data have led to a general scaling feature for the change in $\omega$ of both intershell and intrashell transitions for ions with different nuclear charge $Z$. A similar general feature for the change in $gf$ is also found for the intrashell transition. However, due to the change of the electron correlations between electrons in different shells with respect to the relativistic spin-orbit interaction as $Z$ varies, the variation of $gf$ subject to the surrounding plasma is more complicated for the intershell transition. The results presented in this work may facilitate the plasma diagnostic to determine the plasma temperature and density for the astrophysical objects and the controlled fusion facilities.

Figure 1

The calculated and fitted ratios $R_{\omega }$ of the intrashell transitions T2 and the intershell transitions T1 as functions of the reduced Debye length ${\lambda }_D$ with different $A=\eta \langle r_{1s}\rangle$ and the size parameter $\eta =0,1,2$.

Figure 2

The weights of the main CSFs in $2s^{2}2p3d{}^3{D}_1$ states in terms of the reduced Debye length ${\lambda }_D=Z_{\mathrm{eff}}D$ for C-like (a) Si, (b) Fe, and (c) Kr ions.

Figure 3

The calculated and the fitted ratios $R_{gf}$ of the intrashell transition T2 and the intershell transition T1 as functions of the reduced Debye length ${\lambda }_D$ with different $A=\eta \langle r_{1s}\rangle$ and the size parameter $\eta =0$, 1, and 2.

Figure 4

The ratios $R_{\omega }$ of both T1 and T2 transitions from the C-like ${\mathrm{Ar}}^{12+}$ ion in terms of the plasma electron density $N_e$ with temperature $k_{b}T=400$ eV (black lines), 800 eV (red lines), and 1500 eV (blue lines).