Exclusion principle and nuclear reaction mechanism

Effects of the Exclusion Principle in specific reference to direct reactions are studied in detail by formulating a simple one-dimensional model in the two channel approximation. The fact that a target wavefunction can be described by different systems of cluster wavefunctions on account of the indistinguishability of nucleons is exploited to bring out the connections between the various aspects of the reaction mechanism and the forward and the backward reaction amplitudes. The coupled integro-differential equations of the model are solved by a matrix method, and an iteration method respectively for low and high energies of the incident particle in the entrance channel. The exact solution of the coupled integro-differential equations takes into account the Exclusion Principle and the effects of rescattering and target recoil. The result shows that the direct reactions are long distance or “surface” phenomena. An evidence is presented that this is a consequence of the Exclusion Principle. The exact result is compared with various approximate results. The latter include the cases; 1. antisymmetrization is completely neglected; 2. antisymmetrization is performed on the target wavefunctions only; 3. plane wave Born approximation; 4. distorted wave Born approximation. The result obtained by target antisymmetrization coincides with the exact result only for high energies of the incident particle. The practical use of this result obtained by use of the two equivalent clusterwavefunctions which describe the target wavefunction is discussed in connection with heavy particle stripping.