Adiabatic hyperspherical potentials with localized correlated Gaussians

Abstract

The adiabatic hyperspherical approach is a natural extension of the well-known three-dimensional polar coordinate method to solving a Schr\odinger equation of a few-body system. To evaluate the matrix element of an adiabatic Hamiltonian at a fixed hyper-radius is crucially important in that approach, but due to the difficulty of its calculation real applications have been limited mostly up to four-body systems. To resolve this limitation I introduce a localized hyper-radial function and show that the matrix element needed for $N$-body system can be obtained using correlated Gaussians with arbitrary angular momentum. I demonstrate its feasibility in the systems of $N=3\text{--}6\phantom{\rule{4pt}{0ex}}\ensuremath{\alpha}$ particles. It is pointed out that an extension into correlated Gaussians with double global vectors is desirable for further realistic descriptions of the hyperangular motion.