Orthogonalization of function spaces in the resonating group model

Abstract

A coupled-channel resonating group equation for orthogonal channel spaces is derived. It follows from the common resonating group equation by a recursion relation. The recursion extracts from higher channels all overlaps with lower channels, such that the higher channels become corrections to the lower ones. A physically meaningful definition of elimination potentials becomes possible. The new coupled channel resonating group equation allows the derivation of physical effective potentials by eliminating small corrections, only. It also allows the derivation of technical potentials, i.e. potentials with an unphysical off-shell behaviour, when the dominant part of the equation is eliminated. A numerical example demonstrates that linear dependence of the test function space is not harmful to the new equation.