Finite-element computation of perturbation energies for the two-electron atom

Perturbation energies E₂, E₃, and E₄ in the 1/Z expansion for the ground-state two-electron atom are calculated using accurate representations of the partial waves L=0,1,2,. . . of the first- and second-order eigenfunctions. These are obtained by combining L-Hylleraas basis functions with a one-dimensional finite-element procedure. The contribution to E₂, E₃, and E₄, made by partial waves L{}1, can, with a surprising accuracy, be covered by numerical extrapolation with the help of a Schwartz-type expression in powers of 1/(L+1/2).