Positron Attachment to the He Doubly Excited States

The projection method is used to demonstrate the existence of positron attachment to three doubly excited states of helium. The e⁺He(2s² ¹Sᵉ)deg, e⁺He(3s² ¹Sᵉ), and the e⁺He(2s2p ³Pᵒ) states have binding energies of 0.447, 0.256, and 0.486 eV, respectively. These energies were computed with the stochastic variational method and the configuration interaction method. These states will exist as resonances in the e⁺-He continuum, and the e⁺He(2s² ¹Sᵉ) state could be detectable in the e⁺+He collision spectrum. A resonance width of 0.068 eV was computed for the e⁺He(2s² ¹Sᵉ) state by using the complex rotation method. The existence of a series of e⁺He(ns² ¹Sᵉ) resonances associated with the He(ns²) double Rydberg series is also predicted, and an explicit calculation demonstrating the existence of the e⁺He(3s² ¹Sᵉ) state is reported.