Relativistic Proton-Neutron Quasiparticle-Vibration Coupling Theory with Localized Exchange Terms and Tensor Couplings for Gamow-Teller Resonances and \texorpdfstring{$\beta$}{beta} Decay

Abstract

Abstract

Abstract We develop a relativistic proton-neutron quasiparticle random-phase approximation (pnQRPA) plus proton-neutron quasiparticle-vibration coupling (pnQPVC) model based on localized relativistic Hartree-Fock-Bogoliubov theory with the PCF-PK1 density functional, which incorporates the localized exchange terms and tensor couplings. The localized exchange terms allow the residual interaction, espeically the isovector-pseudovector (tPV) channel, to be determined fully self-consistently without any phenomenological adjustment of the tPV coupling strength. We apply the newly developed relativistic pnQPVC model to the Gamow-Teller (GT) strength distributions in $^{116-134}$Sn and the $\beta^-$-decay half-lives of neutron-rich Ni and Sn nuclei as well as the $N=50$ and $N=82$ isotonic chains. Channel analysis at the pnQRPA and pnQPVC levels demonstrates that the isovector-tensor and tPV channels play key roles in both the GT response and $\beta$-decay half-lives. Beyond pnQRPA, QPVC correlations broaden and redistribute the GT strength, bringing the calculated resonance widths and peak energies into better agreement with experiment. QPVC correlations also substantially reduce the calculated $\beta$-decay half-lives and improve agreement with the experimental data.