Antisymmetrization of a Mean Field Calculation of the T-Matrix
  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 ${\cal A}$ must be included in the definition of the transition operator, $ T\equiv V^\prime{\cal A}+V^\prime{\cal 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. 
A.Wierling, B.G.Giraud, F.Mekideche, H.Horiuchi, T.Maruyama,   A.Ohnishi, J.C.Lemm, A.Weiguny