X iv : n uc l - th / 9 81 10 30 v 3 8 J an 1 99 9 Anharmonic collective excitation in a solvable model

The existence of multiphonon states in the nuclear spectrum of excitation has been predicted since the introduction of collective models [1]. Examples of low-lying nuclear vibrational states have been known for many years in nuclear spectra and are still being actively investigated with new generation of detectors; in particular, two-phonon multiplets and some three-phonon states based on the low-lying collective quadrupole and octupole modes have been found [2–8]. Recently, it has also been beautifully demonstrated that multi-phonon excitations of these low-lying collective vibrations strongly influence heavyion fusion reactions at energies near and below the Coulomb barrier [9], through the socalled fusion barrier distribution analysis [10,11]. It was pointed out that anharmonicities of vibrational excitations can significantly alter the shape of fusion barrier distribution and