1s2s2pP2resonance ofHe−

By using a saddle-point technique, the $1s2s2p{}_{}{}^2{}_{}{}^{}P$ resonance of ${\mathrm{He}}^{-}$ is found to be a Feshbach resonance. It is formed by the strong coupling of [$\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$,$2p$] and [$\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P$,$3d$] configurations. By using a seven-partial-wave 54-term wave function and neglecting the open channels, the energy is -2.149 045 a.u. This is higher than the -2.175 23 a.u. $\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^3{}_{}{}^{}S$ threshold, but significantly below the -2.145 97 a.u. $\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$ threshold. A quasi-projection-operator method is also carried out. Using the same wave function, the energy is -2.150 54 a.u. These results generally agree with that of experiment.