## 3 Results and Discussion  
In Table 1, we give information related to the CI basis used for the various symmetries \({}^{1}\)S,\({}^{1}\)P,\({}^{1}\)D and \({}^{1}\)F. The configuration states, \(\Phi_{n_{1}|1;n_{2}|2}^{(L)}(\mathbf{r}_{1}\mathbf{r}_{2})\), have been constructed according to Equation (5) by one-electron orbitals with angular momenta given in Table 1 and energies sufficiently high to ensure convergence of the results. The order of B-splines was \(k_{b}=9\) with the total number ofB-spline polynomials set at \(n_{b}=110\) for Li\({}^{+}\) and \(n_{b}=170\) for Ne\({}^{9+}\) and Ar\({}^{16+}\). The box radius varied between \(R=50-58\) a.u. for Li\({}^{+}\), \(R=20-28\) a.u. for Ne\({}^{8+}\) and \(R=10-15\) a.u. for Ar\({}^{16+}\). The knot sequence of the spatial grid for the B-spline basis was linear. The two-electron wavefunctions, \(\Phi^{(L)}_{n_{1}l_{1},n_{2}l_{2}}(\mathbf{r}_{1}\mathbf{r}_{2})\), have been constructed from the zero-order configurations by one-electron orbitals with angular momenta given in the mentioned table and energies determined by the indices \(n_{1},n_{2}\) in the following ranges: \(1\leq n_{1}\leq 6\) and \(1\leq n_{2}\leq n_{b}\). The relationship of the indices \(n_{1},n_{2}\) to the energies of the zero-order wavefunctions depends on the basis size parameters such as the maximum value of the box radius as well as the number of B-spline basis functions used. In summary, the whole basis, for each symmetry, resulted in the inclusion of the following number of functions for each ion: 1650-1940 for Li\({}^{+}\), 1600 for Ne\({}^{8+}\) and 2040 for Ar\({}^{16+}\). In Table 2, we show the calculated energies for a few lower bound states of the hydrogenic ions Li\({}^{2+}\), Ne\({}^{9+}\) and Ar\({}^{17+}\). The degree of the agreement with those reported in the National Institute of Standards and Technology (NIST) atomic spectra database [28] is given in the last row of the table. In all cases, the percentage discrepancies of the ground state energies (between the calculated and those of the NIST database) are of the order 0.1% while the excited states are of similar or even smaller order. In Table 3, we show the energy differences of the few lowest states of Li\({}^{+}\), Ne\({}^{8+}\) and Ar\({}^{16+}\) ions with respect to the respective ground state (\(1s^{2}\ {}^{1}S_{0}\)) energy of each ion. In all cases, the percentage discrepancies of the ground state energies (between the calculated and those of the NIST) are of the order 0.1% while the excited states are of similar or even of smaller order. This is not surprising as the role of correlation is more important in the lower energy states, where the electrons are on average closer relative to the higher-energy states. Having examined the reliability of the calculated electronic structure, within the available theoretical and experimental data to compare, we proceed to the main subject of this work: the presentation of ionization cross sections for a range of photon frequencies. In all the following, the horizontal axis in the figures represents the photon energy, given in eV. The cross sections are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**1**\(\mathbf{S}\)** & **1**\(\mathbf{P}\)** & **1**\(\mathbf{D}\)** & **1**\(\mathbf{F}\)** \\ \hline \(s^{2}\) & \(sp\) & \(sd\) & \(sf\) \\ \(p^{2}\) & \(pd\) & \(p^{2}\) & \(pd\) \\ \(d^{2}\) & \(df\) & \(pf\) & \(pg\) \\ \(f^{2}\) & \(fg\) & \(d^{2}\) & \(df\) \\ \(g^{2}\) & & \(dg\) & \(fg\) \\  & & \(f^{2}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: (\(l_{1},l_{2}\)) electronic configurations included in the configuration interaction (CI) calculations for the \({}^{1}L\) symmetries.