Using an asymptotic expansion and the hyperspherical adiabatic approximation, we obtain a representation of the Scrhödinger equation for the helium atom and its isoelectronic ions for large values of the hyper-radius. We solve the lowest-order equation for the channel wave functions with boundary conditions imposed by exchange symmetry. Diagonalization of the potential matrix, keeping only terms through second order in the symmetrized basis set, gives potential curves that show avoided crossings essential for the interpretation of atomic dynamics.

• Received 13 June 1989

DOI:https://doi.org/10.1103/PhysRevA.41.4696