Random phase approximation in a self-consistent covariant approach: recent applications

The relativistic Hartree-Fock (RHF) and Random Phase Approximation (RPA) methods are self-consistently applied to two issues of current interest. The first application is related to the isospin mixing corrections in the problem of super-allowed 0+ → 0+ β-transitions and the unitarity of the CKM matrix. The second application concerns the prediction of inclusive neutrino-nucleus cross-sections, where the results of the present model are compared with other approaches.