The convergent close-coupling method for a Coulomb three-body problem

The close-coupling method relies on the reformulation of the Schrödinger equation into an infinite set of coupled-channel equations by expanding over the complete set of target states. The difficulty in applying this approach is that the continuum channels are known to be very important in the intermediate-energy region and coupling to them must be included with little approximation. We discuss the application of the convergent close-coupling (CCC) method which allows the continuum to be treated in a systematic manner via the use of square-integrable states. The CCC method utilizes an expansion of the target in a complete set of orthogonal L2 functions which form a basis for the underlying Hilbert space. The utility of the method relies on being able to demonstrate convergence in the scattering amplitudes of interest as the basis size is increased