Modifications of the optical potential formalism arising from the pauli principle

Abstract

An extension of the unsymmetrized Feshbach optical potential formalism for two-fragment elastic scattering which fully incorporates the Pauli principle is obtained. The optical potential is defined in terms of an arbitrary off-shell extension of the multichannel transition operators in such a way as to preserve the simple two-body description of the elastic scattering characteristic of the unsymmetrized formalism. This is in contrast to definitions based upon the explicit restriction of the problem to the fully antisymmetrized Hilbert space. Conditions for the occurrence of discrete singularities of the optical potential are derived and for the off-shell extension introduced by Alt, Grassberger and Sandhas it is found that these singularities are correlated with resonance structure of the scattering amplitude with the correct physical characteristics. It is shown that neither Pauli-forbidden resonance nor continuum states appear in the spectral representation of the optical potential.