Doubly excitedPeandDoFeshbach resonances in the lithium isoelectronic sequence

The Feshbach projection method and the generalized saddle-point technique have been used to obtain energies of ${}_{}{}^{4,2}{}_{}{}^{}$ ${\mathit{P}}^{\mathit{e}}$ and ${}_{}{}^{4,2}{}_{}{}^{}$ ${\mathit{D}}^{\mathit{o}}$ Feshbach resonances in ${\mathrm{He}}^{\mathrm{-}}$, Li, and ${\mathrm{Be}}^{+}$. The results from both methods confirm each other. Positions and Auger energies of 31 resonances (3 in ${\mathrm{He}}^{\mathrm{-}}$, 14 in Li, and 14 in ${\mathrm{Be}}^{+}$) lying between the 2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ and 3 ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ thresholds are given. These data can serve as a basis for identification of those resonances in future experiments. Some suggestions for such experiments are made.