TRANSLATIONALLY-INVARIANT CLUSTERS IN COORDINATE SPACE - HIGHER-ORDERCLUSTERS AND THE GAUSSIAN EXPANSION BASIS

We develop and apply a series of extensible and flexible cluster expan sions, tailored specifically to few-body systems. Our analysis begins by recalling previous work which examined the role of the centre-of-ma ss (CM) motion in the few-body system. We show how the problems genera ted by the cm motion generally associated with correlated wavefunction s can be explicitly avoided altogether, and from the outset, by restri cting the excitations induced to those which leave the cm undisturbed. This is accomplished by expressing all correlation functions solely i n terms of relative coordinates. All such functions are expanded in ba ses of Gaussians, which are shown to be highly efficient computational ly. Applications to the H-3 and He-4 nuclei are presented. Results sho w that the method produces both accurate energies and wavefunction pro perties.