  In an effort to find an effective interaction which can consistently be used
for both the mean-field part and the residual part in beyond mean-field
theories, properties of the Skyrme interactions as a residual interaction are
investigated. The time-dependent density-matrix theory (TDDM) is used as a
beyond mean-field theory and the ground states of $^{16}$O and $^{40}$Ca are
calculated using the five standard parametrizations of the Skyrme interaction
which differs in density and momentum dependence. It is found that the Skyrme
interaction which has strong density dependence and weak momentum dependence
induces substantial ground-state correlations comparable to the results of
other theoretical calculations.
