Energy Expression for the Metal Cluster

We found that a minimum in the full energy appears if we renormalize the energy expression by making the frequency factor Huia in Eq. (73) depend on the deformation parameter r, using the following prescription fiu o — fiwo(l + nr)-1, where n is the number of vibrational quanta. This form of the corrective factor is justified, for it results from the expansion of q n = e nT for small r  

At this stage of our research this renormalization seems a little bit intuitive, but we think that there exist deep physical reasons for its choice and this is the aim of our present investigation. 

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