In view of the advances of knowledge, both experimental and theoretical, about hadronic scattering processes at high energies, the potential-theory model studied before is found to exhibit a number of realistic features. Because partial differential equations can be dealt with in a much more straightforward manner than operator equations, this potential-theory model is useful in understanding some features of high-energy processes. The problem of exponentiation, i.e., the possible appearance of an exponential factor, is studied in detail. It is found that the simple-exponentiation form, found recently in field theories within certain approximations, does not hold in general when the scattering particles have a finite size or internal degrees of freedom. This result in turn is applied to the field-theoretical cases to understand further the nature of the approximations involved.