Accuracy of three-body wave functions obtained with the correlation-function hyperspherical-harmonic method.

Abstract

The local convergence and accuracy of wave functions obtained by direct solution of the Schr\"odinger equation with the help of the correlation-function hyperspherical-harmonic method are analyzed for ground and excited states of the helium atom and for the ground state of the positronium negative ion. The inclusion of the cusp conditions into the correlation function is shown to be of crucial importance, not only near the coalescence points, but also away from them. The proper inclusion of all cusps yields for the ground state of the helium atom the local wave-function accuracy of about ${10}^{\mathrm{\ensuremath{-}}7}$ for different interparticle distances. The omission of one of the cusps in the excited helium atom reduces the wave-function precision to ${10}^{\mathrm{\ensuremath{-}}2}$ near the corresponding coalescence point and to ${10}^{\mathrm{\ensuremath{-}}4}$--${10}^{\mathrm{\ensuremath{-}}5}$ away from it.