Long-range couplings in the adiabatic hyperspherical basis

The infinite set of coupled equations in the adiabatic hyperspherical representation of two-electron correlated states is solved in the asymptotic region. The solution reveals that the longest-range couplings represent a partial transformation to independent-electron coordinates. Simple corrections to the phase shifts of ${\mathrm{H}}^{\mathrm{-}}$ are obtained. Adiabatic and corrected phase shifts in the monopole approximation are compared with the Hartree-Fock phase shifts. Good agreement is obtained. The correction is applied to previously reported adiabatic phase shifts.