SHELL STRUCTURES AND CHAOS IN NUCLEI AND LARGE METALLIC CLUSTERS

A reflection-asymmetric deformed oscillator potential is analyzed from the classical and quantum mechanical point of view. The connection be tween occurrence of shell structures and classical periodic orbits is studied using the ''removal of resonances method'' in a classical anal ysis. In this approximation, the effective single particle potential b ecomes separable and the frequencies of the classical trajectories are easily determined. It turns out that the winding numbers calculated i n this way are in good agreement with the ones found From the correspo nding quantum mechanical spectrum using the particle number dependence of the fluctuating part of the total energy. When the octupole term i s switched on it is found that prolate shapes are stable against chaos and can exhibit shells where spherical and oblate cases become chaoti c. An attempt is made to explain this difference in the quantum mechan ical context by leaking at the distribution of exceptional points whic h results from the matrix structure of the respective Hamiltonians. In a similar way we analyze the modified Nilsson model and discuss its c onsequences for metallic clusters.