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

Abstract

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 $\ensuremath{\rho}$-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, $^{48}\mathrm{Ca},\phantom{\rule{0.28em}{0ex}}^{78}\mathrm{Ni},\phantom{\rule{0.28em}{0ex}}^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. 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 $\ensuremath{\beta}$-decay half-lives of $^{78}\mathrm{Ni}$ and $^{132}\mathrm{Sn}$ are also calculated and found to be decreased by a factor of $\ensuremath{\sim}2$ by the inclusion of the new phonons.