Nuclear $beta$-decay half-lives in the relativistic point-coupling model

The self-consistent proton-neutron quasiparticle random phase approximation approach is employed to calculate $beta$-decay half-lives of neutron-rich even-even nuclei with $8leqslant Z leqslant 30$. A newly proposed nonlinear point-coupling effective interaction PC-PK1 is used in the calculations. It is found that the isoscalar proton-neutron pairing interaction can significantly reduce $beta$-decay half-lives. With an isospin-dependent isoscalar proton-neutron pairing strength, our results well reproduce the experimental $beta$-decay half-lives, although the pairing strength is not adjusted using the half-lives calculated in this study.