Global Calculation of Nuclear Shape Isomers

To determine which nuclei may exhibit shape isomerism, we use a well-benchmarked macroscopic-microscopic model to calculate potential-energy surfaces as functions of spheroidal (epsilon(2)), hexadecapole (epsilon(4)), and axial-asymmetry (gamma) shape coordinates for 7206 nuclei from A=31 to A=290. We analyze these and identify the deformations and energies of all minima deeper than 0.2 MeV. These minima may correspond to characteristic experimentally observable shape-isomeric states. Shape isomers mainly occur in the A=80 region, the A=100 region, and in an extended region centered around (208)Pb. We compare our model to experimental results for Kr isotopes. Moreover, in a plot versus N and Z we show for each of the 7206 nuclei the calculated number of minima. The results reveal one fairly unexplored region of shape isomerism, which is experimentally accessible, namely the region northeast of (208)(82)Pb.