Evaluation of differential cross-sections for light element reactions at low energies using R-matrix calculations: The case of 12C

Abstract

The theoretical evaluation of diÆerential cross-section values for low-energy re- actions of light elements is of great importance in the fields of IBA (Ion Beam Analysis) and nuclear astrophysics. R-matrix theory is generally accepted as the most appropriate one for the analysis of resonance reactions in low-energy nuclear physics. In this approach, the configuration space of the scattering problem is divided into an internal region, corresponding to the compound nucleus, where the total wave function can be expanded into a complete set of eigenstates (in terms of unknown base functions, with the energy eigenvalues and the matrix elements of the base functions being adjustable parameters) and an external region, where the possible combinations of coupled particle pairs exist, corresponding to the reaction channels that emerge from the compound nucleus. This division of space is made by the choice of the boundary of the compound nucleus, i.e. an appropriate nuclear radius is chosen for each reaction channel. The R-matrix takes account of all the interactions which occur inside the nucleus. In the present work, results obtained in the specific case of elastic scattering and charged-particle nuclear reactions, namely for the 12C+p system are presented.