Analytical functions for the calculation of hyperspherical potential curves of atomic systems - art. no. 032508

We present angular basis functions for the Schrodinger equation of two-elec tron systems in hyperspherical coordinates. By using the hyperspherical adi abatic approach, the wave functions of two-electron systems are expanded in analytical functions, which generalizes the Jacobi polynomials. We show th at these functions, obtained by selecting the diagonal terms of the angular equation, allow efficient diagonalization of the Hamiltonian for all value s of the hyperspherical radius. The method is applied to the determination of the S-1(e) energy levels of the Li+ and we show that the precision can b e improved in a systematic and controllable way.