Universal shapes of fermion clusters in the local density approximation.

Using the density functional Kohn-Sham method we show that the internal shapes of fermion clusters are nearly independent of the interparticle interactions. The odd-even staggering of the total energy of small nuclei and of sodium clusters are shown to be of the same origin. Tetrahedral deformations are predicted for 40, 70 and 112 atom sodium clusters. An alternative model for linear nuclei is suggested. [ABSTRACT FROM AUTHOR]