Comparison of hyperspherical versus common-reaction-coordinate close-coupling methods for ion-atom collisions at low energies

We present detailed comparisons between the two quantal approaches—hyperspherical close-coupling and common-reaction-coordinate close-coupling methods—on an exemplary case of He²⁺+H(1s) collisions at center-of-mass energy from 20 eV up to 1.6 keV. It is shown that the partial-wave charge-transfer cross sections from the two approaches agree very well at low energy below 200 eV down to 30 eV. This good agreement is a strong indication of the validity of both methods. The small difference at very low energies and the convergence with respect to the number of channels in both approaches at higher energies are also discussed.