Weighted projection and optimization of coupled-channel equations

Abstract

The conventional coupled-channel method for many-particle scattering is modified to facilitate applications to low-energy collision processes and to break-up (ionization) reactions. A new approach to the construction of coupled-channel equations is developed in terms of the weighted projections, where proper choices of the weighting function can simplify the set of coupled equations. Optimal choices of the weighting functions are discussed, and several approximations for construction of the weight functions are presented. The conventional pseudostate and mixed basis expansions are shown to be related to the weighted projection approach. The break-up (and ionization) channels can be included in the coupled-channel approach. Finally, the recently developed generalization of the Hartree - Fock (GHF) theory for scattering is shown to be a special case of the weighted projections, thus providing a partial justification of the use of amputated wavefunctions for the continuum state projection.