Summing pomeron trees

It is argued that multi-pomeron exchange diagrams not involving pomeron loops play a dominant role in the presently accessible energy range. These diagrams are explicitly summed for a pomeron pole with intercept larger than one (in the limit α'=0) s-channel unitarity is automatically satisfied (but not saturated). For particle-particle scattering phenomenological features are obtained in agreement with the data (sigmasub(T), sigmasub(el), (dlog sigmasub(el)/dt)/sub(t=0) increase to a finite limit and sigmasub(el)/sigmasub(T) can be made arbitrarily small). The results are also applied to nucleus-nucleus scattering. (Auth.)