Using the particle-vibration coupling for particles moving in the harmonic oscillator potential, the anharmonicity in two-phonon states of monopole, dipole, and quadrupole giant resonances of shape vibrations is studied. The anharmonic term in both the energy and strength of two-phonon giant resonances vanishes in the leading order of ${N}_{F}\ensuremath{\gg}1.$ Thus, instead of ${A}^{\ensuremath{-}1},$ the calculated energy shift becomes the order of ${A}^{\ensuremath{-}4/3},$ which is still the order of ${A}^{1/3}$ larger than that obtained from a macroscopic description of the vibrations.
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