Theoretical study of the ${\mathrm{C}}^{-}$ ${}^4{S}_{3/2}^o$ and ${}^2{D}_{3/2,5/2}^o$ bound states and C ground configuration: Fine and hyperfine structures, isotope shifts, and transition probabilities

This work is an ab initio study of the $2p^3\hspace{0.5em}{}^4{S}_{3/2}^o$, and ${}^2{D}_{3/2,5/2}^o$ states of ${\mathrm{C}}^{-}$ and $2p^2\hspace{0.5em}{}^3{P}_{0,1,2}$, ${}^1{D}_2$, and ${}^1{S}_0$ states of neutral carbon. We use the multiconfiguration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all ${\mathrm{C}}^{-}$ detachment thresholds, including correlation effects to about $0.5\%$. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intraconfiguration transition probabilities are also estimated.

Figure 1

Levels diagram of C and ${\mathrm{C}}^{-}$. The fine structures of C ${}^{3}P$ and ${\mathrm{C}}^{-}$${}^2{D}^o$ terms are magnified ($\times 100$).

Figure 2

Bilogarithmic plot of the convergence of the C(${}^{3}P$) mass polarization expectation value versus the corresponding energy in hartrees. The coordinates of the black squares are the differences (in absolute value) between the results of the MR-I$\lceil \mathit{nl}\rceil$ and MR-I$\lceil 12k\rceil$ calculations, $n=6$–11 from left to right. Similarly, the coordinates of the white squares show the convergence of MR${}_p$-I$\lceil 12k\rceil$ toward MR${}_{99.95}$-I$\lceil 12k\rceil$, $p=(99$–99.9)% from left to right.