Effects of ground-state correlations on dipole and quadrupole excitations of ${}^{40}$Ca and ${}^{48}$Ca

The effects of ground-state correlations on the dipole and quadrupole excitations are studied for ${}^{40}$Ca and ${}^{48}$Ca using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Large effects of the ground-state correlations are found in the fragmentation of the giant quadrupole resonance in ${}^{40}$Ca and in the low-lying dipole strength in ${}^{48}$Ca. It is discussed that the former is due to a mixing of different configurations in the ground state and the latter is from the partial occupation of the neutron single-particle states. The dipole and quadrupole strength distributions below 10 MeV calculated in ERPA are in qualitatively agreement with experiment.