Energies and widths of (${1s}^{2}3l{3l}^{\prime }$) resonant states of ${\mathrm{C}}^{2+}$, ${\mathrm{N}}^{3+}$, ${\mathrm{O}}^{4+}$, and ${\mathrm{Ne}}^{6+}$

We report theoretical results for autoionizing states of systems with a closed-shell core and that lie above several ionization thresholds. The energy positions and widths are given for the (${1s}^{2}3l{3l}^{\prime }$) ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^{1,3}{}_{}{}^{}P$ resonant states of the ${\mathrm{C}}^{2+}$, ${\mathrm{N}}^{3+}$, ${\mathrm{O}}^{4+}$, and ${\mathrm{Ne}}^{6+}$ ions, which are of great experimental interest at the present moment. Our results show that a generalization of the method of F. Martín et al. [Europhys. Lett. 4, 799 (1987); J. Chem. Phys. 87, 6635 (1987)] provides a very useful and simple procedure to obtain energy positions and resonance widths, as well as the contributions of the different continua to the width.