Intercombination transition rates in ${\mathrm{N}}^{+}$

Accurate intercombination transition rates ($A$), arising from the $2s^{2}2pnl$ ($n$ = 3, 4, 5; $l$ = $s,p,d$) and $2s2p^3$ configurations of ${\mathrm{N}}^{+}$, are reported. Wavefunctions for the studied states in ${\mathrm{N}}^{+}$ are determined using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method and account for the effects of valence, core-valence (CV), and core-core (CC) correlations. It is found that the combined CV and CC correlation effects are important for accurate predictions of intercombination rates of ${\mathrm{N}}^{+}$. A strong spin-orbit mixing between the states ${}^{3}P_1^o$ and ${}^{1}P_1^o$ of $2s^{2}2p3s$ causes that the intercombination rates on its states ${}^{1,3}P_1^o$ are exceedingly sensitive to electron correlations and other corrections. The strong visible intercombination lines of ${\mathrm{N}}^{+}$ arise from the $2s^{2}2p3s-2s^{2}2p3p$ and $2s^{2}2p3p-2s^{2}2p3d$ transitions. There are also strong infrared and ultraviolet intercombination lines that have important applications in plasma diagnosis of radiative cooling coefficient and abundance. Different systematic methods are used to evaluate the intercombination rates and their uncertainties. For relatively strong lines ($gf>0.01$) of $2s^{2}2p3l$($l$ = $s,p,d$), $2s^{2}2p4l$($l$ = $s,p,d$) and $2s^{2}2p5s$ the uncertainties are separately estimated to be within 7%, 12%, and 20%. The rates of extremely weak lines, $gf<{10}^{-6}$, are of interests in the temperature and density diagnostic in nebulae, but are remarkably difficult to accurately calculate. The present calculations have included appropriate electron correlations to deal with them and provide guidance for further studies.

Figure 1

The effects of combined CV and CC correlations as well as the Breit interaction on the intercombination rates. $Y$ axis is the changing tendency of transition rates in different correlation models, i.e., $\frac{|A_X-A_{(X-1)}|}{A_{(X-1)}}$, where $X$ is 7SDV, 7SDVC, 7SDVCB, 7SDVCBQ; ($X-1$) corresponds to 6SDV, 7SDV, 7SDVC, 7SDVCB.

Figure 2

(a) The uncertainties ($100{\delta }_A$) of intercombination $A$ of $2s^{2}2p^2-2s2p^3$ of ${\mathrm{N}}^{+}$. (b) The rate ratio $\frac{A_{\text{other}}}{A_{\text{this}}}$. (c) The assessments of the influences of some higher-order correlations. The tab “1,2,…,16” from left to right in (a, b, c) indicates 16 lines of $2s^{2}2p^2-2s2p^3$ listed in Table 4.