  Using an eikonal analysis, we examine the validity of the factorization
theorem for nucleon-nucleon, gamma p and gamma gamma collisions. As an example,
using the additive quark model and meson vector dominance, we directly show
that for all energies and values of the eikonal, that the factorization theorem
sigma_{nn}/sigma_{gamma p} = sigma_{gamma p}/sigma_{gamma gamma} holds. We can
also compute the survival probability of large rapidity gaps in high energy
pbar p and pp collisions. We show that the survival probabilities are identical
(at the same energy) for gamma p and gamma gamma collisions, as well as for
nucleon-nucleon collisions. We further show that neither the factorization
theorem nor the reaction-independence of the survival probabilities depends on
the assumption of an additive quark model, but, more generally, depends on the
opacity of the eikonal being independent of whether the reaction is n-n, gamma
p or gamma gamma.
