Abstract
The saddle-point complex-rotation method is tested for a three-electron system by calculating the ${(1s2s2s)}^{2}S$ resonance in ${\mathrm{He}}^{\ensuremath{-}}$, Li I, Be II, and B III. The energy position and width obtained for this resonance are well converged for a wide range of rotation angles and nonlinear parameters for all atomic systems considered. To obtain higher accuracy, the relativistic and mass polarization corrections are also calculated. The results are compared with those of the most accurate theoretical calculations and experiments. For Be II, the agreement between the theoretical widths is very poor. Experimental data are needed to confirm the correct theoretical value.
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