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 alpha '=O). s-channel unitarity is automatically satisfied (but not saturated). For particle-particle scattering phenomenological features are obtained in agreement with the data ( sigma /sub T/, sigma /sub el/, (d log sigma /sub el//dt) mod /sub t=0/ increase to a finite limit and sigma /sub el// sigma /sub T/ can be made arbitrarily small). The results are also applied to nucleus-nucleus scattering. (9 refs).