Shell structures and chaos in nuclei and large metallic clusters

Abstract

A reflection-asymmetric deformed oscillator potential is analyzed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the "removal of resonances method" in a classical analysis. In this approximation, the effective single particle potential becomes separable and the frequencies of the classical trajectories are easily determined. It turns out that the winding numbers calculated in this way are in good agreement with the ones found from the corresponding quantum mechanical spectrum using the particle number dependence of the fluctuating part of the total energy. When the octupole term is switched on it is found that prolate shapes are stable against chaos and can exhibit shells where spherical and oblate cases become chaotic. An attempt is made to explain this difference in the quantum mechanical context by looking at the distribution of exceptional points which results from the matrix structure of the respective Hamiltonians. In a similar way we analyze the modified Nilsson model and discuss its consequences for metallic clusters.