General eikonal theory of quantal scattering

A general description of eikonal theory is given in the form of a self-consistent and exact formalism involving an effective Hamiltonian. Such a Hamiltonian may be used as an approximation in the treatment of high-energy potential scattering. The approach is similar to those of Sugar and Blankenbecler (1969) and of Osborn (1970), but with an important difference which involves making the correct distinction between the wavevector which is the free parameter of the theory and that which is associated with the eigenvalue of the Hamiltonian. The result is a more precise statement of the unitarity and reciprocity theorems and obviates the need for the 'Glauber rotation anzatz' if the free parameter is chosen so as to restore true energy conservation to an elastic s-matrix element. Furthermore the resulting wavefunctions are more suitable for use in distorted-wave theories than the more usual ones.