Antisymmetrized Lippmann-Schwinger equations and optical potentials

A recent study of the effect of the Pauli principle in elastic nuclear scattering uses the prior off-shell extension for the multichannel transition operators to derive antisymmetrized Lippmann-Schwinger equations, while such equations are shown not to exist if the off-shell extension due to Alt, Grassberger, and Sandhas is employed instead. We show that the limitations associated with this second off-shell extension are inconsequential for all physical considerations. New physically constrained antisymmetrized Lippmann-Schwinger equations are found in terms of a simple effective interaction which incorporates all of the effects of the Pauli principle and whose properties are explicit. These equations, which are based on the Alt et al. off-shell extension, are employed to obtain in a direct manner the antisymmetrized generalization of the Feshbach formalism for the two fragment optical potential