POTENTIAL-HARMONIC EXPANSION FOR ATOMIC WAVE-FUNCTIONS

One way to reduce the large degeneracy of the hyperspherical-harmonic basis for solving few- and many-body bound-state problems is to introduce an optimal basis truncation called the potential-harmonic (PH) basis. In this paper we introduce various potential-harmonic truncation schemes and assess their accuracies in predicting the energies of the helium and H- ground states and the excited 2(1)S level of the helium atom. We first find that the part of the PH basis that accounts for one-body correlations gives a better ground-state energy for He than Hartree-Fock (2.8790 a.u. versus 2.8617 for Hartree-Fock and 2.9037 exact). When an orthogonal complement is introduced to the basis to account for e-e correlations, we find that the error in the binding energy is 0.000 25 a.u., and 0.000 15 a.u. for ground-state and excited helium, and 0.000 35 a.u. for H-. Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the hyperspherical-harmonic method useful for systems with N > 3.