The Axial Charge Renormalization in a Relativistic Description of Finite Nuclei

Starting from a realistic One-Boson-Exchange model of the nucleon nucleon interaction the relativistic mean field for nucleons is determined within the Dirac Brueckner Hartree Fock approach for finite nuclei. The matrix elements of the axial charge operator evaluated for the solutions of the Dirac equation with this selfenergy are investigated. These matrix elements are enhanced with respect to the equivalent non relativistic ones obtained from the solutions of the Schr\'odinger equation with the non relativistic equivalent potential. The present results confirm at a qualitative level the results for the axial charge renormalization obtained with perturbative approaches. However, the results obtained differ in size from those of the perturbative approach and are nucleus and state dependent