Projection operator study of heavy-ion reactions below the Coulomb barrier and its application to 12C + 12C

The ('12)C+('12)C reaction is studied below the Coulomb barrier. After a brief review of the current status a model termed the "generalized doorway" model is proposed. Within the framework of this model each doorway is taken to consist of parts of the elastic channel, the single excitation channel and the mutual excitation channel. The excitations are treated in terms of the rotational model. Projection operator techniques are used to extract the resonance parameters of the doorways. Theoretical calculations are performed for the structure factor and the cross sections to the most important exit channels of the ('12)C+('12)C reaction. The non-resonant part of the structure factor is found to provide the major contribution to the ('12)C+('12)C reaction in the energy region of astrophysical importance. A comparison has been made for the case where the nuclear potential has a soft repulsive core and the case when the core is absent. The implications of this study on astrophysics are discussed. At various stages of the work a comparison of the results of the calculations and the experimental findings have been made.