Doubly excited nonautoionizing P , D , and F states of helium with Coulomb and screened Coulomb potentials

We have investigated the doubly excited 1,3Pᵉ, 1,3Dᵒ, and 1,3Fᵉ nonautoionizing states of helium atom with Coulomb and screened Coulomb (Yukawa) potentials in the framework of Ritz variational principle. Highly accurate correlated exponential wave functions with exponents generated by a quasirandom process are used to represent the correlation effect. For the Coulomb case, the metastable bound-excited $2pnp$ ¹Pᵉ (3≤n≤5), $2pnp$ ³Pᵉ (2≤n≤5), $2pnd$ 1,3Dᵒ (3≤n≤9), and $2pnf$ 1,3Fᵉ (4≤n≤9) states energies are reported. Our upper-bound results for the $2pnd$ ¹Dᵒ (3≤n≤7), $2pnf$ ¹Fᵉ (4≤n≤8), ³Dᵒ and ³Fᵉ states are the lowest values up to this date. For the screened Coulomb case, the lower-lying metastable bound states energies for different screening parameters and for each spin states are also reported.