  We investigate giant resonances of spherical nuclei on the basis of the
Argonne V18 potential after unitary transformation within the Similarity
Renormalization Group or the Unitary Correlation Operator Method supplemented
by a phenomenological three-body contact interaction. Such Hamiltonians can
provide a good description of ground-state energies and radii within
Hartree-Fock plus low-order many-body perturbation theory. The standard Random
Phase Approximation is applied here to calculate the isoscalar monopole,
isovector dipole, and isoscalar quadrupole excitation modes of the 40Ca, 90Zr,
and 208Pb nuclei. Thanks to the inclusion of the three-nucleon interaction and
despite the minimal optimization effort, a reasonable agreement with
experimental centroid energies of all three modes has been achieved. The role
and scope of the Hartree-Fock reference state in RPA methods are discussed.
