Antisymmetrization of a Mean Field Calculation of the T-Matrix

Abstract

The usual definition of the prior(post) interaction $V(V^{\prime })$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector $\mathcal{A}$ must be included in the definition of the transition operator, $T\equiv V^{\prime }\mathcal{A}+V^{\prime }\mathcal{A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ scattering, making use of self consistent symmetries.

Comments: 30 pages, no figures, plain TeX, SPHT/93/144