Fully self-consistent calculation of β-decay half-lives within Skyrme energy density functional

β -decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA). The self-consistency is addressed, in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states. First, the impact of J² terms on the β -decay half-lives is investigated by using the SGII interaction, revealing a large influence. Subsequently, numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII, LNS, SKX, and SAMi. Finally, comparisons to available experimental data and predictions of different theoretical models are discussed.