On the Effect of Pauli Principle on Collective Vibrations in Nuclei

The earlier theories of collective vibrations based on the Random Phase Approximation have neglected the effect of the Pauli principle. A method to take into account this effect is developed for the simple model with the pairing plus Q-Q interactions. It is shown that the correction is appreciable on the properties of the vibrational states. The effect is found to be particularly important for a vibrational state with low frequency. This fact plays an essential role in reproducing the experimental mass number dependence of the energies of the vibrational states. The numerical calculations are carried out for the first vibrational 2+ states of even nuclei. The results agree remarkably well with the experimental systematics for these nuclei with a constant strength of the Q-Q interactions.