Global $\beta$-decay half-life predictions in a quasiparticle random-phase approximation based on relativistic Hartree-Fock Bogoliubov model with localized exchange terms

Abstract We present systematic calculations of nuclear $\beta^-$-decay half-lives for 5456 nuclei with $8\leq Z\leq120$, covering even-even, odd-$A$, and odd-odd ones, within the self-consistent proton-neutron quasiparticle random-phase approximation (pnQRPA) based on localized relativistic Hartree-Fock-Bogoliubov (RHFB) theory with the PCF-PK1 interaction. The Fierz transformation is employed to localize the exchange terms, ensuring a self-consistent treatment of the nuclear ground state and the particle-hole residual interaction for the calculation of excited states, while the isoscalar tensor coupling yields a relatively large Landau effective mass of $M_L^*=0.85M$. Spherical and allowed Gamow-Teller approximations are adopted, and the isoscalar proton-neutron pairing strength is determined as an isospin-dependent function of $N-Z$ by fitting experimental half-lives. The calculated half-lives reproduce the experimental systematics reasonably well, with about 80\% of the nuclei lying within one order of magnitude of the experimental data. The deviation decreases systematically toward shorter-lived nuclei, reaching standard deviation $\sigma=0.329$ for $T_{1/2}^{\rm Exp.}<0.1$ s, comparable to the corresponding RHB+pnQRPA calculations with D3C$^*$ and FRDM+QRPA results. Pronounced deviations are found around shell closures and in deformed regions, highlighting the importance of correlations beyond QRPA level, deformation effects and the first-forbidden transitions. Finally, the gated recurrent unit network, with PCF-PK1 results as inputs, reduces the overall standard deviation to 0.171 orders of magnitude for 690 nuclei whose experimental and calculated half-lives are both shorter than $10^{6}$ s, corresponding to a 83.6\% reduction relative to PCF-PK1 results.