Effect of deformations on the binding energy of centrally depressed nuclei

Abstract

The energy density formalism is implemented to study the binding energy of some heavy, superheavy and hyperheavy nuclei. The macroscopic contribution of binding energy is derived in the presence of a depression parameter in the nuclear density distribution, and the total energy is obtained by adding the shell and pairing correction to the macroscopic part. Total energy is studied with the variation of quadrupole and hexadecapole deformation parameters using different values of depression parameter. The addition of the shell and pairing corrections affects the behavior of the total energy especially the minimum position at specific deformation parameters, a second minimum in some cases are close to the first one, suggesting the possible existence of shape isomers. We minimized the total energy with respect to deformation and density depression parameters and obtained the binding energy of 208Pb, 238U, 252Cf, 280Cn, , 298Fl, 306120, 320126, 339136, 500174 and 700226. The binding energies obtained are in good agreement with the available experimental data. The difference between the binding energies obtained by this simple method and experimental ones is less than 0.13%.