Electronic shell structure of large metallic clusters in the modified harmonic oscillator

Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular and chaotic behavior in terms of energy, deformation and strength of the $(\vec L)^2$ term has been found. According to this law, shell structure survives for higher particle numbers only with lesser deformation.