The adiabatic hyperspherical approach is a natural extension of the well-known three-dimensional polar coordinate method to solving a Schrodinger 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 = 3-6 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.
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