New class of antisymmetrized optical potentials

This paper is mainly concerned with the construction and various properties of a new class of antisymmetric, two-fragment, elastic scattering optical potentials. The construction is based directly on the wave function formulation of $N$-particle collision theories, which are antisymmetrized herein using the method of Adhikari and Glöckle. Those theories which are label transforming are considered first. For such theories, the resulting optical potentials are asymmetric but nevertheless real for energies below the inelastic threshold $E_{\mathrm{inel}}$, and are asymmetric and absorptive for $E\ge E_{\mathrm{inel}}$. This unusual feature of asymmetry is a consequence of working directly with $N$-particle collision theories, almost all of which are expressed in non-Hermitian matrix form, and arguments are presented as to why asymmetry is not a practical problem. Not only are the new class of optical potentials asymmetric, it is also found that exchange effects generally enter them in an extremely simple fashion. These latter two features distinguish the members of the new class from the optical potential developed recently by Goldflam and Kowalski. Examples of label-transforming theories producing such potentials are the extended Faddeev theory of Levin, the precursor form of the Bencze, Redish, Sloan theory, and the wave function component theory of L'Huillier, Redish, and Tandy. Their existence establishes that formalisms other than those based on the Alt, Grassberger, Sandhas transition operator lead to symmetrized optical potentials free of elastic unitarity cuts, albeit potentials which are not Hermitian analytic. In addition to the above theories, a new, symmetrized form of the equations of the channel permuting array theory is developed.