Generalized eikonal approximation

A new approximation method for potential scattering is proposed. The usual idea of linearizing propagators in eikonal approximation is incorporated with the second Born approximation in this method such that the scattering amplitude retains more accurate low order Born terms. Consequently, the linearized propagator is dependent on the specifics of the potential. The new formula thus obtained gives spectacular improvements to usual eikonal formulas. Interestingly it works also for scatterings at not so high energy.