Feshbach and Shape Resonances in thee-HP1System

Abstract

Using a Born-Oppenheimer-type expansion for the two-electron wave functions in hyperspherical coordinates, three potential curves are obtained for ${\mathrm{H}}^{-}$ ${}_{}{}^1{}_{}{}^{}P$ states converging to the $n=2\mathrm{}$ state of the hydrogen atom. It is shown that the Feshbach resonances are associated with one curve and the shape resonance with another. The connections with the "+" and "-" classification of helium doubly excited states and with the asymptotic dipole-field representation of ${\mathrm{H}}^{-}$ are discussed.