Shell structure for deformed nuclear shapes

Eigenvalues for the harmonic oscillator without 1.s or 12 terms suggest a deformed shell structure for nuclei with axes ratios 2 : 1 and deformation 0.6 with corresponding nucleon ''magic numbers'' 2, 4, 10, 16, 28, 40, 60, 80, 110, 140, subject to small modifications due to spin-orbit and other correction terms. Experimental evidence of reasonably stable, highly deformed structures corresponding to nucleon numbers 16, 20, 28, 40, and 60 (64) is presented. Attempts to calculate the corresponding potential energy surfaces using the Strutinsky shell corection method are described. The method turned out to be unsuccessful in the region of Zr and Mo isotopes. The main difficulty is that the liquid-drop energy surface rises too steeply for the larger deformations for this region of nuclei to allow any secondary minima. (S.B.)