# Extended Photoionization Cross Section Calculations for C III
## 2 Computation Methods and Results
### Atomic Structure Calculation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**orb** & **1s** & **2s** & **3s** & **4s** & **5s** & **2p** & **3p** & **4p** \\ \hline \(\lambda\) & 1.2898 & 0.9946 & 0.9842 & 0.9842 & 1.0000 & 0.8702 & 0.8667 & 8.1200 \\ \hline
**orb** & **5p** & **3d** & **4d** & **5d** & **4f** & **5f** & **5g** & \\ \hline \(\lambda\) & 1.0000 & 0.7898 & 48.120 & 1.0000 & 1.1600 & 1.0000 & 1.0000 & \\ \hline \end{tabular}
\end{table} 
Table 1: Values of the adjustable parameters used in SUPERSTRUCTURE to compute the one-electron orbitals. \begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{1}{c}{_Bound Orbitals_} & \multicolumn{2}{c}{\(N\)-electron} & \multicolumn{2}{c}{\((N+1)\)-electron} \\ _Included_ & \multicolumn{2}{c}{_Configuration Data_} & \multicolumn{2}{c}{configuration data_} \\ _Symmetries_ & _Couplings_ & Symmetries Couplings & Symmetries Couplings \\ \hline
10 & 4 & 9 & 22 & 173 \\ \hline
15 & 5 & 14 & 30 & 488 \\ \hline \end{tabular}
\end{table} 
Table 2: Models of calculation. The intermediate coupling frame transformation approach entails transforming unphysical S- or K-matrices (within the framework of the multichannel quantum defect theory) to a jK-coupling scheme [36]. In the external R-matrix region, the code STGB is used to identify the J-resolved bound states of Be-like Carbon, which lie below the Li-like ground state. Table 3 shows the comparison with other theoretical calculation results on some bound states 1s\({}^{2}2 snl\) and 1s\({}^{2}2 pnl\) (n \(<\) 10) for J = 0\({}^{\rm e}\) and 1\({}^{\rm o}\) levels, in cm\({}^{-1}\). Results are provided relative to the C IV 1s\({}^{2}\)2s ground states when compared with the Breit-Pauli \(R\)-matrix plus pseudo-state close-coupling calculation (RMPS) [28], and relative to the C III 1s\({}^{2}2s^{2}\) ground state when compared to NIST listing [35]. Compared to previous theoretical works and to the NIST listing, it can be seen that the present theoretical results determined via the Breit-Pauli \(R\)-matrix method show very good agreement. Uncertainty in the energy determination in the present work has been reduced by almost an order of magnitude with the use of suitable correlated target and scattering wavefunctions. Figure 1: Comparison of computed energy levels in this study, with values from the NIST database, for CIV. The red stars indicate the \(-\)0.25 percent maximum relative discrepancies with the first model calculation. The black star symbols indicate +0.12 maximum discrepancies with the second model calculation. No., as the label in the \(x\)-axis, corresponds to the number of the first 24 levels of C IV according to the NIST listings. Figure 2: Present theoretical radiative transition probabilities, A values in s\({}^{-1}\) (BPRM), plotted against the NIST values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(E\) (cm\({}^{-1}\))} & \multicolumn{2}{c}{\(E\) (cm\({}^{-1}\))} & \multicolumn{2}{c}{\(E\) (cm\({}^{-1}\))} & \multicolumn{2}{c}{\(E\) (cm\({}^{-1}\))} \\ \multicolumn{2}{c}{**J = 1\({}^{o}\)**} & **Relative to** & **Relative** & **Relative to** & **Relative to** & **Relative to** & **\%** \\ \multicolumn{2}{c}{**Levels**} & **1s\({}^{2}\)2s** & **to** & **to** **1s\({}^{2}\)2s** & **to** & **1s\({}^{2}\)2s\({}^{2}\)** & **to** & **(cm\({}^{-1}\))** \\ \multicolumn{2}{c}{**BPRM**} & **RMPS** & & **BPRM** & **NIST** & \\ \hline
1s\({}^{2}\)2s2p \({}^{3}P_{1}^{o}\) & \( \begin{array}{c}-332,894.8\\ 894.8\end{array} \) & 1.7224 & \(-\)333,688 & 1.7204 & 52,694 & 52,390.75 & 5.78\({}^{-03}\) \\ \hline
2s2p \({}^{1}P_{1}^{o}\) & \( \begin{array}{c}-281,386.5\\ 386.5\end{array} \) & 1.8734 & \(-\)283,424 & 1.8667 & 104,202.9 & 102,352.04 & 1.80\({}^{-02}\) \\ \hline
2s3p \({}^{1}P_{1}^{o}\) & \( \begin{array}{c}-126,926.2\\ 926.2\end{array} \) & 2.7894 & \(-\)127,216 & 2.7863 & 258,663.2 & 258,931.29 & \(-\)1.03\({}^{-03}\) \\ \hline
2s3p \({}^{3}P_{1}^{o}\) & \( \begin{array}{c}-126,257.9\\ 257.9\end{array}