The dipole isovector M3 sum rule in the random phase approximation

Abstract We have worked out the random phase approximation (RPA) M 3 , dipole isovector sum rule for complete Skyrme forces. Detailed results obtained with this kind of forces are presented for several nuclei. We discuss the contribution to M 3 of the different terms entering the Skyrme functional. Our exact RPA results are used to test different approximations made in the past.