Three-alpha final state interactions with Faddeev theory

Abstract

We have considered an exactly soluble model which describes the breakup of a parent particle into three identical, spinless, structureless daughter particles. Using this model the breakup of a 2+ particle with final state interactions dominated by two-body resonances has been studied. The two-body resonances were chosen to correspond to the ground and first excited states of Be8 and the parent particle to correspond to the 18.37 MeV. state of C12. The model treats the interaction which initiates the breakup to first order and the strong final state interactions to all orders. The strong interactions are described by equations of the Faddeev type with separable two-body interactions in order to make the problem numerically tractable. In Chapter II the development of the integral equation, the partial wave decomposition and the reduction using the separable t-matrix approximation are given. Chapter III contains a discussion of the two-body interactions used to generate the separable t-matrix and in Chapter IV the form taken for the initial bound state breakup vertex is presented. Numerical methods for the solution of the integral equations are described in Chapter V; in Chapter VI, results of calculations and the comparison with the experimental findings are presented and discussed. Some reasonable extensions and improvements of the model are outlined in Chapter VII; Chapter VIII contains a summary and the conclusions. Details of the angular momentum decomposition are treated in Appendix A, and Appendix B contains the details of the laboratory coordinate system and the necessary kinematics.