The eigenenergies for ³S excited states of the helium atom with CFPHGLF method

The matrix elements of the correlation function between symmetric potential harmonics were first simplified into the analytical summation of the grand angular momentum. The correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF) proposed by us recently was then applied to directly solve the Schrödinger equation for n³S(n=2–5) excited states of the helium atom. With only 12 PHs, the convergent eigenenergies of 2³S, 3³S, 4³S and 5³S states were 2.17427, 2.06849, 2.03644, 2.02257 E_h, respectively. The errors only were 0.00096, 0.00020, 0.00007, 0.00005 Eh, when compared with the exact Hylleraas variational results respectively.