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

Abstract

Graphical representations of three-particle wave functions obtained by direct solution of the Schr\odinger equation with the correlation-function hyperspherical-harmonic (CFHH) method are obtained and analyzed for ground and excited states of the helium atom and for the ground state of the \ensuremath{\mu}dd mesomolecular ion. The inclusion of adequate singular and cluster-correlation behavior is shown to be of crucial importance for a proper description of the wave function. In the CFHH method the wave function is a product of a correlation function and of a smooth factor expanded into hyperspherical-harmonic (HH) functions. While the HH expansion by itself is not able to reproduce a correct form of the wave function, the inclusion of the correlations results in its proper description even for low values of the maximal global momenta ${\mathit{K}}_{\mathit{m}}$.