  The analytic properties of Nilsson's Modified Oscillator (MO), which was
first introduced in nuclear structure, and of the recently introduced, based on
quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator
(3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce
correctly in terms of only one parameter the magic numbers of alkali clusters
up to 1500 (the expected limit of validity for theories based on the filling of
electronic shells), are considered. Exact expressions for the total energy of
closed shells are determined and compared among them. Furthermore, the
systematics of the appearance of supershells in the spectra of the two
oscillators is considered, showing that the 3-dim q-HO correctly predicts the
first supershell closure in alkali clusters without use of any extra parameter.
