Exact multiple scattering theory of two-nucleus collisions including the Pauli principle

Abstract

Exact equations for two-nucleus scattering are derived in which the effects of the Pauli principle are fully included. Our method exploits a modified equation for the scattering of two identical nucleons, which is obtained at the beginning. Considering proton-nucleus scattering we found that the resulting amplitude has two components, one resembling a multiple scattering series for distinguishable particles, and the other a distorted ($A\ensuremath{-}1$) nucleon cluster exchange. For elastic $\mathrm{pA}$ scattering the multiple scattering amplitude is found in the form of an optical potential expansion. We show that the Kerman-McManus-Thaler theory of the optical potential could be easily modified to include the effects of antisymmetrization of the projectile with the target nucleons. Nucleus-nucleus scattering is studied first for distinguishable target and beam nucleus. Afterwards the Pauli principle is included, where only the case of deuteron-nucleus scattering is discussed in detail. The resulting amplitude has four components. Two of them correspond to modified multiple scattering expansions and the others are distorted ($A\ensuremath{-}1$)- and ($A\ensuremath{-}2$)- nucleon cluster exchange. The result for $d\ensuremath{-}A$ scattering is extended to the general case of nucleus-nucleus scattering. The equations are simple to use and as such constitute an improvement over existing schemes.