# Extended Photoionization Cross Section Calculations for C III
## 2 Computation Methods and Results  
### Atomic Structure Calculation  
The present work is similar to the use of the R-matrix method for calculating photoionization cross sections of various atoms and ions. The calculation has been performed based on the well-known Breit-Pauli R-matrix numerical method (BPRM). Details of the theoretical background for the R-matrix method, photoionization, and the BPRM suite of codes can be found, for example, in refs. [29; 30; 31; 32; 33]. Two sets of theoretical calculations were performed to check the validity of our atomic structure model. The SUPERSTRUCTURE (SS) [30; 31] has been used to calculate orbital parameters, \(\lambda_{nl}\), variationally determined by optimizing the weighted sum of the term energies. The first model includes nine 1s\({}^{2}\)\(nl\) (\(n=2\)-4, \(l=s\), p, d, f) target states, represented in terms of ten orthonormal basis orbitals. At this stage we used the scaling parameters obtained by the Opacity Project team [34]. The (\(N+1\))-electron correlation for CIII includes all possible configurations with 2s\({}^{2}\),2p\({}^{2}\),3s\({}^{2}\),3p\({}^{2}\),3d\({}^{2}\) and 4s,4p,4d,4f. The second model calculation extends the first one to construct accurate wavefunctions of the \(N\)-electron target states belonging to C IV. Fifteen orthogonal, one-electron orbitals \(nl\) (\(n=1\)-5, \(l=0\)-4)were used. The values of the scaling parameters obtained following the minimization procedure are shown in Table 1. Table 2 presents the configuration data included in the two calculation models. The maximum total angular momentum \(L\) for the \((N+1)\)-electron \(LS\)-coupling Hamiltonian was set to 6 in the first model and at 8 in the second one. This enables the computation up to \(J=5\). The \(R\)-matrix calculations were carried out in the intermediate coupling scheme by including the spin-orbit interaction terms of the Breit-Pauli Hamiltonian. The number of continuum basis orbitals used to express the wavefunction in the inner region of the \(R\)-matrix code was varied between 20 and 35, and the results were analyzed. We noticed that increasing the number of basic functions does not necessarily improve the results. It was decided to use 30 continuum basis orbitals in all calculations. The effect of varying the size of the \(R\)-matrix inner region radius has been investigated, and a value of 17.8 atomic units was chosen for numerical stability and convergence. The maximum \(LS\)-coupling Hamiltonian matrix size was about 400 in the first model calculation, and these \(LS\)-coupling symmetries give rise to \(J\)-resolved matrices of order 1470. The intermediate coupling calculations were carried out on recoupling the \(LS\) symmetries in a pair-coupling representation in stage RECUPD. The (e + ion) Hamiltonian matrix was diagonalized for each resulting \(J^{\pi}\) in STGH. The fine, structure-bound levels were sorted through the poles in the \((e+\text{ion})\) Hamiltonian with a fine mesh of effective quantum number \(\
u\). The mesh of 0.00002 has been used in the calculation. Figure 1 shows, for completeness, the percentage difference between calculated and experimental C IV target level energies. Both models indicate the 2p state energy of C IV at 0.59 Ryd above the ground with a relative discrepancy of \(\pm 1.05\) percent with respect to the NIST value [35]. Comparing the present results with the observed values, despite the 1.05 percent difference found for 1s\({}^{2}\)2p levels, we found that overall, the average percent difference across the corresponding NIST \(J^{\pi}\) symmetries was up to 0.12 percent. We adopted these results for the scattering calculation. As a measure of the accuracy of the wavefunction and energy values, the transition probabilities have also been considered. The calculated and experimental A-values (in s\({}^{-1}\)) were plotted in Figure 2 on a logarithmic versus logarithmic scale to incorporate the various magnitudes of results.