PLANE-WAVE APPROXIMATION FOR THE SCATTERING AMPLITUDE

Abstract

Different methods of calculating the S-wave scattering amplitude using the plane-wave approximation are discussed. The resulting scattering amplitudes satisfy the unitarity condition and for high energies approach the Born approximation asymptotically. These methods are applied to the special class of potentials that can be expressed as an infinite sum of exponential potentials, and in particular to some potentials for which the exact solutions are known. It is found that imposing the unitarity condition on the Born approximation, in general, does not improve the result of the calculation.