Large Shell Model Calculations for Calcium Isotopes: Spectral Statistics and Chaos

We perform large shell model calculations for Calcium isotopes in the full fp shell by using the realistic Kuo–Brown interaction. The Calcium isotopes are especially interesting because the nearest–neighbour spacing distribution P (s) of low–lying energy levels shows significant deviations from the predictions of the Gaussian Orthogonal Ensemble of random–matrix theory. This contrasts with other neighbouring nuclei which show fully chaotic spectral distributions. We study the chaotic behaviour as a function of the excitation energy. In addition, a clear signature of chaos suppression is obtained when the single–particle spacings are increased. In our opinion the relatively weak strength of the neutron-neutron interaction is unable to destroy the regular single–particle mean–field motion completely. In the neighbouring nuclei with both protons and neutrons in valence orbits, on the other hand, the stronger proton-neutron interaction would appear to be sufficient to destroy the regular mean–field motion.