Coupling charge-exchange vibrations to nucleons in a relativistic framework: effect on Gamow-Teller transitions and beta-decay half-lives

The nuclear response theory for isospin-transfer modes in the relativistic particle-vibration coupling framework is extended to include coupling of single nucleons to isospin-flip (charge-exchange) phonons, in addition to the usual neutral vibrations. This new coupling introduces dynamical pion and rho-meson exchange, beyond the Hartree-Fock approximation, up to infinite order. We investigate the impact of this new mechanism on the Gamow-Teller response of a few doubly-magic neutron-rich nuclei, namely $^{48}$Ca, $^{78}$Ni, $^{132}$Sn and $^{208}$Pb. It is found that the coupling to isospin-flip vibrations can have a non negligible impact on the strength distribution and quenching of the giant resonance, globally improving the agreement with the experimental data. The corresponding beta-decay half-lives of $^{78}$Ni and $^{132}$Sn are also calculated, and found to be decreased by a factor $\sim 2$ by the inclusion of the new phonons.