Pairwise infall velocity and acceleration in the Zel'dovich approximation

Using perturbative methods, nonlinear corrections to the mean pairwise infa ll velocity and acceleration are investigated both in the Zel'dovich approx imation and in the higher order Eulerian perturbation theory. We calculate the second-order corrections to these two quantities, and find that for a t ypical cold-dark-matter model, predictions of the Zel'dovich approximations are considerably different from that of the Eulerian perturbation theory, even on quasi-linear scales. This is an important caveat against the applic ation of this approximation to quantities closely related to the dynamical nature of structure formation.