Doubly excited states of the helium negative ion

Abstract

Wave functions of doubly excited states ${}_{}{}^2{}_{}{}^{}S$, ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}P$, ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}D$ of the $n=2\mathrm{}$ shell of ${\mathrm{He}}^{-}$ are studied in hypersherical coordinates. The interaction between the outer electron pair and the ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ open-shell core is treated by imposing boundary conditions at the core's surface and by spin recoupling. Adiabatic potential curves and the corresponding eigenvectors are studied as functions of the hyperradius $R$. Complex effects of channel couplings are analyzed, particularly for the ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ states. Resonant "free-free" radiative transitions ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ and ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}\to {}_{}{}^4{}_{}{}^{}P$ are calculated and analyzed into contributions from the dipole operator at different $R$.