If the (effective) central potential is replaced with an (effective) azimuthal potential, (V(r, z)), depending independently on

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If the (effective) central potential is replaced with an (effective) azimuthal potential, \(V(r, z)\), depending independently on the polar radius \(r\) in a plane and on the height \(z\) along the axis transverse to the plane, is it possible to have a shell model? Why? If so, consider the harmonic oscillator potential with different constants in the direction \(z\) and in the polar radial direction \(r\), and find the (first few) magic numbers.

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