Failure of the Eikonal Approximation for the Vertex Function in a Boson Field Theory

By an explicit calculation of the high-energy behavior of the three-point function in the $\lambda {\phi }^3$ theory, through terms of order ${\lambda }^5$, we demonstrate that the eikonal approximation for generalized ladder exchange fails in that model, for this vertex function. In a given order, it underestimates the exact asymptote.