Coupling charge-exchange vibrations to nucleons in a relativistic framework: Effect on Gamow-Teller transitions and β-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, ${}^{48}\mathrm{Ca},{}^{78}\mathrm{Ni},{}^{132}\mathrm{Sn}$, 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 $\beta$-decay half-lives of ${}^{78}\mathrm{Ni}$ and ${}^{132}\mathrm{Sn}$ are also calculated and found to be decreased by a factor of $\sim 2$ by the inclusion of the new phonons.

Figure 1

Coupling of nucleons to (a) neutral and (b) CE phonons.

Figure 2

PVC interaction with coupling to neutral (wiggly lines) and CE (springs) phonons.

Figure 3

${\mathrm{GT}}^{-}$ strength distributions in ${}^{48}\mathrm{Ca},{}^{132}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$. The dashed black, full blue, and full red curves show the results obtained within pn-RRPA, pn-RTBA with coupling to neutral ($N$) phonons, and pn-RTBA with coupling to neutral and CE phonons, respectively. The green points show the available experimental data [33, 34, 35, 36].

Figure 4

${\mathrm{GT}}^{-}$ strength in ${}^{132}\mathrm{Sn}$ with $\mathrm{\Delta }=200\mathrm{keV}$ for different truncations of the spectrum of CE phonons $\left\{\lambda \right\}$. See the text for details.

Figure 5

${\mathrm{GT}}^{-}$ strength distribution in ${}^{78}\mathrm{Ni}$ (top) and cumulative integrated strength (bottom) with $\mathrm{\Delta }=200\mathrm{keV}$.