Combined hyperspherical and close-coupling description of two-electron wave functions: Application toe−−Helastic-scattering phase shifts

A new procedure for matching hyperspherical coordinate (HS) wave functions onto close-coupling (CC) wave functions for two-electron systems at a hyperradius $R=R_0$ is shown to give agreement with accurate ${}_{}{}^1{}_{}{}^{}S$ phase shifts for $e+\mathrm{H}$ up to the ${2s}^2$ resonance. The procedure uses far fewer basis functions than are required in either a HS or a CC calculation alone. The strengths of each method are thus effectively combined to obtain wave functions describing highly correlated two-electron motion near the nucleus ($R<\mathrm{}{R}_0$) and largely independent electron motion away from the nucleus ($R>\mathrm{}{R}_0$).