Application of random-phase approximation to vibrational excitations of double-Lambda hypernuclei

Using the Hartree-Fock plus random phase approximation (HF + RPA), we study the impurity effect of Lambda hyperon on the collective vibrational excitations of double-Lambda hypernuclei. To this end, we employ Skyrme-type Lambda N and Lambda Lambda interactions for the HF calculations, and the residual interactions for the RPA are derived with the same interactions. We find that the inclusion of two Lambda hyperons in O-16 shifts the collective states toward higher energies. In particular, the energy of the giant monopole resonance of 18 O-18(Lambda Lambda), as well as that of Pb-210(Lambda Lambda), becomes higher. This implies that the effective incompressibility modulus increases owing to the impurity effect of Lambda particles, if the beta-stability condition is not imposed.