It is well-known that a better description of the spin-flip response,such as the magnetic dipole response and Gamow-Teller response shall enable more reliable predictions for neutral-current neutrino nucleus cross sections for supernova explosion[1]andβ-decay half-lives of very neutron-rich nuclei.In this report,we study the spin-flip response of finite nuclei in a fully self-consistent Hartree-Fock plus random phase approximation within the SLy5Skyrme parameter set[2-3].We discuss the effect of J2 terms and2 It is well-known that a better description of the spin-flip response, such as the magnetic dipole response and Gamow-Teller response shall enable more reliable predictions for neutral-current neutrino nucleus cross sections for supernova explosion [1] and β-decay half -lives of very neutron-rich nuclei. In this report, we study the spin-flip response of finite nuclei in a fully self-consistent Hartree-Fock plus random phase approximation within the SLy5Skyrme parameter set [2-3]. We discuss the effect of J2 terms and2