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One way to reduce the large degeneracy of the hyperspherical-harmonic basis for solving fewand many-body bound-state problems is to introduce an optimal basis truncation called the potentialharmonic (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 '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 0.00025 a.u. , and 0.00015 a.u. for ground-state and excited helium, and 0.00035 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 X)3. PACS number(s): 31.15.+q

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A direct solution of the Schrodinger equation for the 2 'S, 3 '5, 4 'S, and 5 'S states of the helium atom is obtained with the correlation-function hyperspherical-harmonic (CFHH) method. Given the proper correlation function chosen from physical considerations, the method generates wave functions accurate in the whole range of interparticle distances that lead, in turn, to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results show that even with the simplest correlation function, the accuracy of the CFHH method (which contains no adjustable parameters) for excited states is comparable to that of the ground state. The accuracy is also comparable to that of the most sophisticated variational calculations involving hundreds of variational parameters.PACS number(s): 31.15.+ q, 31.50.+w