Precise nonvariational calculation of excited states of helium with the correlation-function hyperspherical-harmonic method

A direct solution of the Schrödinger equation for the 2 ${}_{}{}^1{}_{}{}^{}$S, 3 ${}_{}{}^1{}_{}{}^{}$S, 4 ${}_{}{}^1{}_{}{}^{}$S, and 5 ${}_{}{}^1{}_{}{}^{}$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.