Combinatorial calculations of nuclear level densities, spin projections, and nuclear deformation

Calculations similar to those previously used for a spherical nucleus were performed at various deformations ranging in some cases from δ=-0.5 to δ=1.0. The states for each spin projection (K) were ordered according to energy to avoid crossing of states with same spin projection and parity. The corresponding energies of the ordered sets for each deformation were considered as the energy vs deformation for particular states. Energies at intermediate deformations were obtained using a cubic interpolation. Energy minima and their associated deformations were determined for each state. States often have more than one energy minimum indicating the presence of shape isomers as illustrated in the cases of ¹⁶⁶Ho and ²⁴⁰Pu. In the former, a prolate and an oblate minimum exist which persist at higher energies. In the latter, a second prolate minimum is observed where the fission isomer is expected. Differences in energy gaps are discernible in the various minima. A plot of the deformations corresponding to the energy minima of the lowest energy states for each spin projection (the yrast levels) vs the spin projection reveals that the model nucleus becomes more oblate as the spin projection increases. The change in oblateness contains discontinuities. A plot of these yrast deformations vs the yrast energies for various nuclides indicates an apparent independence of the kind or size of the nuclide. The "best" G's (pairing parameters) for some nuclides were determined by fitting the level densities to the experimental values at the neutron binding energies. The results for deformed nuclei are compared with the earlier results obtained for spherical nuclei.[NUCLEAR STRUCTURE ⁴⁰Ca, ¹¹⁴Cd, ¹⁶⁶Ho, ²⁴⁰Pu; calculated levels vs spin projection and deformation, yrast levels, deduced pairing parameters. Nilsson levels, BCS pairing.]