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

We present systematic calculations of nuclear β⁻-decay half-lives for 5456 nuclei with 8≤ Z≤120, 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 ML^*=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 σ=0.329 for T1/2Exp.<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 10⁶ s, corresponding to a 83.6% reduction relative to PCF-PK1 results.