Translationally invariant clusters in coordinate space: higher-order clusters and the Gaussian expansion basis

We develop and apply a series of extensible and flexible cluster expansions, tailored specifically to few-body systems. Our analysis begins by recalling previous work which examined the role of the center-of-mass (CM) motion in the few-body system. We show how the problems generated by the CM motion generally associated with correlated wavefunctions can be explicitly avoided altogether, and from the outset, by restricting the excitations induced to those which leave the CM undisturbed. This is accomplished by expressing all correlation functions solely in terms of relative coordinates. All such functions are expanded in bases of Gaussians, which are shown to be highly efficient computationally. Applications to the 3H and 4He nuclei are presented. Results show that the method produces both accurate energies and wavefunction properties. (author)