Magic numbers, metal-cluster harmonic

Reproduction of metal-cluster magic numbers using a -deformed, 3-dimensional, harmonic oscillator model... 

Recently it has been shown [21] that the spectrum of this g-deformed, 3-dimensional harmonic oscillator (Q30) reproduces very well that of the modified harmonic oscillator introduced by Nilsson [12, 15] without the spin-orbit coupling term. Since the Nilsson model without spin-orbit coupling is essentially the Nilsson-Clemenger model used for the description of metal clusters [11], it is worth examining whether the Q30 model can be used to reproduce the magic numbers and some other properties of simple metal clusters. 

Indeed it has been found [22] that Q30 (which follows ug(3) D sog(3) symmetry) yields correctly all magic numbers experimentally observed for alkali metal clusters up to 1500, the expected limit of validity for theories based on the filling of electronic shells [4], This indicates that u,(3), which is a nonlinear deformation of the u(3) symmetry describing the 3-dimensional isotropic (spherical) harmonic oscillator, is a good candidate for describing the symmetry of alkali metal clusters. 

We have shown how to derive potentials which, when put into the standard Schrodinger equation, provide approximately the same spectrum as the q-deformed, 3-dimensional harmonic oscillator. In the present work, we have also found prescriptions for choosing the model parameters r and A, thus closing the procedure for obtaining magic numbers. This could be very useful in further investigations on other properties of metal clusters. 

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