Constrained correlated-Gaussians for hyperspherical calculations

We formulate a hyperspherical approach within standard configuration interaction calculations aiming at a description of large-scale dynamics of $N$-particle system. The channel wave function and the adiabatic channel energy are determined by solving a hyperradius-constrained eigenvalue problem of the adiabatic Hamiltonian. The needed matrix elements are analytically evaluated using correlated Gaussians with good orbital angular momentum and parity. The feasibility of the approach is tested in three-$\alpha$ system. A spectrum of the adiabatic channel energies is determined depending on the degree of localization of the basis functions.