Sum rule approach to a soft dipole mode in Λ hypernuclei

Applying the sum rule approach, we investigate the energy of a soft dipole motion in Λ hypernuclei, which results from a dipole oscillation of a Λ hyperon against the core nucleus. To this end, we systematically study single-Λ hypernuclei, from Λ16O to Λ208Pb, for which the ground-state wave function is obtained in the frame-work of Hartree-Fock method with several Skyrme-type ΛN interactions. Our results indicate that the excitation energy of the soft dipole Λ mode, E_sdΛ, decreases as the mass number increases. We find that the excitation energy is well parametrized as E_sdΛ=26.6A^-1 ^/3+11.2A^-2^/3 MeV for the SkM* NN interaction and E_sdΛ=21.3A^-1^/3+22. 6A^-2^/3 MeV for the SIII NN interaction as a function of mass number A.