Confined helium: Excited singlet and triplet states

Energies for the first four singlet and triplet S states of a helium atom confined at the center of an impenetrable sphere are reported. All calculations used explicitly correlated Hylleraas basis sets. The first triplet state is shown to lie below the first excited singlet state only when the confinement radius is greater than 0.988_a0$0.988a_0$. A simple configuration interaction calculation was performed in parallel with Hylleraas calculation. The one-electron atomic orbitals of the configuration treatment provide insight into the physical concepts behind the numerical results of the Hylleraas treatment. This was particularly helpful in understanding the level crossing and avoided crossings observed with changing confinement radius.